Description: UTF-8-encoding
Forwarded: not-needed
 Patch certain files with iconv to convert from national encoding.
Author: Camm Maguire <camm@debian.org>

---
The information above should follow the Patch Tagging Guidelines, please
checkout http://dep.debian.net/deps/dep3/ to learn about the format. Here
are templates for supplementary fields that you might want to add:

Origin: <vendor|upstream|other>, <url of original patch>
Bug: <url in upstream bugtracker>
Bug-Debian: https://bugs.debian.org/<bugnumber>
Bug-Ubuntu: https://launchpad.net/bugs/<bugnumber>
Forwarded: <no|not-needed|url proving that it has been forwarded>
Reviewed-By: <name and email of someone who approved the patch>
Last-Update: 2021-01-27

Index: acl2-8.4dfsg/axioms.lisp
===================================================================
--- acl2-8.4dfsg.orig/axioms.lisp
+++ acl2-8.4dfsg/axioms.lisp
@@ -16858,7 +16858,7 @@ evaluated.  See :DOC certify-book, in pa
 ; Without the setting of custom:*default-file-encoding* for clisp in
 ; acl2.lisp, the build breaks with the following string (note the accented "i"
 ; in Martin, below):
-;   Francisco J. Martn Mateos
+;   Francisco J. Martín Mateos
 ; With that setting, we do not need an explicit :external-format argument for
 ; the call of with-open-file in acl2-check.lisp that opens a stream for
 ; "acl2-characters".
Index: acl2-8.4dfsg/books/defexec/dag-unification/dag-unification-l.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/dag-unification-l.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/dag-unification-l.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; dag-unification-l.lisp
-;;; Ttulo: A dag based unification algorithm
+;;; Título: A dag based unification algorithm
 ;;; ============================================================================
 
 #| To certify this book:
@@ -22,7 +22,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
Index: acl2-8.4dfsg/books/defexec/dag-unification/dag-unification-rules.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/dag-unification-rules.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/dag-unification-rules.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; dag-unification-rules.lisp
-;;; Ttulo: Unification rules on term dags
+;;; Título: Unification rules on term dags
 ;;; ============================================================================
 
 #| To certify this book:
@@ -21,7 +21,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
Index: acl2-8.4dfsg/books/defexec/dag-unification/dag-unification-st.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/dag-unification-st.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/dag-unification-st.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; dag-unification-st.lisp
-;;; Ttulo: A dag based unification algorithm using stobjs
+;;; Título: A dag based unification algorithm using stobjs
 ;;; ============================================================================
 
 #| To certify this book:
@@ -21,7 +21,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
@@ -571,7 +571,7 @@
 
 ;;; Guard verification:
 
-;;; REPETIDOS  LOS DEJO?
+;;; REPETIDOS ż LOS DEJO?
 
 
 (local
@@ -1176,7 +1176,7 @@
 
 ;;; Guard verification
 
-;;; AVERIGUAR POR QU ESTE TEOREMA TARDA TANTO!!!!!!!!
+;;; AVERIGUAR POR QUé ESTE TEOREMA TARDA TANTO!!!!!!!!
 
 
 ;;; I don't know why, but the following theory has an important
Index: acl2-8.4dfsg/books/defexec/dag-unification/dags.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/dags.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/dags.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; dags.lisp
-;;; Ttulo: Term dags in ACL2
+;;; Título: Term dags in ACL2
 ;;; ============================================================================
 
 #| To certify this book:
@@ -18,7 +18,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
@@ -510,7 +510,7 @@
 	(not (dag-p-aux hs rp g)))))
 
 ;;; Finally, the soundness theorem:
-;;; 
+;;; ·······························
 
 (defthm dag-p-soundness
   (implies (not (dag-p g))
@@ -554,7 +554,7 @@
 
 
 ;;; The main lemma for completeness:
-;;; 
+;;; ································
 
 (local
  (defthm dag-p-aux-completeness-main-lemma
@@ -1601,7 +1601,7 @@
 
 
 ;;; RECALL: These two theorems would allow us to define functions like these:
-;;; 
+;;; ·········································································
 
 
 ; (defun occur-check-l (flg x h g)
Index: acl2-8.4dfsg/books/defexec/dag-unification/list-unification-rules.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/list-unification-rules.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/list-unification-rules.lisp
@@ -1,5 +1,5 @@
 ;;; ============================================================================;;; list-unification-rules.lisp
-;;; Ttulo: Unification as transformation rules
+;;; Título: Unification as transformation rules
 ;;;         (using a  prefix representation of terms)
 ;;; ============================================================================
 
@@ -17,7 +17,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
Index: acl2-8.4dfsg/books/defexec/dag-unification/matching.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/matching.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/matching.lisp
@@ -89,9 +89,9 @@
 ;;; ----------------------------------------------------------------------------
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.1 How we deal with selection.
-;;; 
+;;; ············································································
 
 
 ;;; Firs we prove that equal-set is a congruence w.r.t. the second
@@ -139,9 +139,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.2 transform-subs-sel preserves the set of matchers.
-;;; 
+;;; ············································································
 
 
 (local
@@ -211,7 +211,7 @@
 	      (not (matcher sigma S)))))
 
 ;;; The three main theorems of this subsubsection
-;;; 
+;;; ·············································
 
   (defthm transform-subs-sel-preserves-matchers-1
     (implies
@@ -235,10 +235,10 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.3 (system-substitution (cdr S-match)) is an invariant in the rules
 ;;;     of transformation.
-;;; 
+;;; ············································································
 
 
 
@@ -261,9 +261,9 @@
      (system-substitution (cdr (transform-subs-sel S-match)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.4 Main property of the property system-substitution
-;;; 
+;;; ············································································
 
 
 (local
@@ -362,7 +362,7 @@
 			(length-term nil args2))))))
 
 ;;; And the main result:
-;;; 
+;;; ····················
 
   (defthm transform-subs-sel-decreases-length-of-first-system
     (implies (not (normal-form-syst S-match))
@@ -460,7 +460,7 @@
 
 ;;; Three lemmas to state that the set of matchers is preserved by
 ;;; subs-system-sel
-;;; 
+;;; ··········································································
 
 (local
  (defthm subs-system-sel-preserves-matchers-1
@@ -488,7 +488,7 @@
 (in-theory (enable union-systems))
 
 ;;; subs-system-sel preserves the property of being a system-substitution.
-;;; 
+;;; ··································································
 
 (local
  (defthm subs-system-sel-preserves-system-substitution
@@ -496,7 +496,7 @@
 	   (system-substitution (cdr (subs-system-sel S-match))))))
 
 ;;; Guard verification: a substitution-s-p is returned
-;;; 
+;;; ···················································
 
 (local
  (defthm
@@ -604,7 +604,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 
 (defthm subs-sel-soundness
@@ -618,7 +618,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ············
 
 
 (defthm subs-sel-completeness
@@ -632,7 +632,7 @@
 
 ;;; Closure property:
 ;;; (the following theorem is needed for guard verification)
-;;; 
+;;; ························································
 
 
 (defthm matching-sel-substitution-s-p
Index: acl2-8.4dfsg/books/defexec/dag-unification/subsumption-subst.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/subsumption-subst.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/subsumption-subst.lisp
@@ -26,15 +26,15 @@
 ;;; Our goal is to define the subsumption relation between
 ;;; substitutions. In the literature, this relation is defined in this
 ;;; way:
-;;;     sigma <= delta iff (exists gamma) gammasigma = delta
-;;; where "" stands for composition.
+;;;     sigma <= delta iff (exists gamma) gamma·sigma = delta
+;;; where "·" stands for composition.
 
 ;;; Note that equality between substitutions is functional equality (we cannot
 ;;; use equal), so we reformulate this property as:
 
 ;;; (*) sigma <= delta iff (exists gamma)
 ;;;                        s.t. for all term
-;;;                        gammasigma(term) = delta(term)
+;;;                        gamma·sigma(term) = delta(term)
 
 
 ;;; Our goal in this book is to define the subsumption relation between
@@ -285,9 +285,9 @@
 ;;; if (subs-sust sigma delta)
 ;;; WE DISTINGUISH THREE CASES.
 
-;;; 
+;;; ············································································
 ;;; 3.1.1 Case 1: x is a variable outside V
-;;; 
+;;; ············································································
 
 
 
@@ -303,14 +303,14 @@
    :hints (("Goal" :in-theory (enable x-not-in-domain-remains-the-same)))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.1.2. Case 2: x is a variable of (domain-var sigma)
-;;; 
+;;; ············································································
 
 
 ;;; 3.1.2.1 A lemma for this case 2:
 ;;; subs-subst composed with sigma is equal to delta in V.
-;;; 
+;;; ······················································
 
 (local
  (encapsulate
@@ -373,7 +373,7 @@
 (local (in-theory (disable subs-subst matching-subst)))
 
 ;;; 3.1.2.2 Another lemma for case 2:
-;;; 
+;;; ·······························
 
 (local
  (defthm variables-co-domain-var
@@ -383,7 +383,7 @@
 
 
 ;;; 3.1.2.3 The main result for Case 2
-;;; 
+;;; ································
 
 (local
  (defthm
@@ -396,14 +396,14 @@
 		   (val x delta)))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.1.3. Case 3: x in V but not in (domain-var sigma)
-;;; 
+;;; ············································································
 
 
 ;;; 3.1.3.1 A lemma for Case 3
 ;;; In this case, matching and matching-subst-r take the same values.
-;;; 
+;;; ·································································
 
 (local
  (defthm
@@ -472,7 +472,7 @@
 
 
 ;;; With terms and list of terms (not only with variables)
-;;; 
+;;; ······················································
 
 (local
  (defthm
@@ -512,7 +512,7 @@
 ;;; following version will be used as a rewrite rule.
 
 ;;; With terms but without using composition
-;;; 
+;;; ········································
 
 (defthm
   subs-subst-implies-matching-subst-r-appplied-to-sigma-term-is-delta-term
@@ -526,7 +526,7 @@
 
 
 ;;; With respect to subsumption between terms
-;;; 
+;;; ·········································
 
 
 ;;; Trivial consequence of completeness of subsumption and the previous
@@ -563,7 +563,7 @@
 ;;; existence of two substitutions, called sigma-w and delta-w and the
 ;;; only property we will assume about them is that sigma-w <=
 ;;; delta-w. That is, exists another substitution gamma-w such that
-;;; delta-w = gamma-wsigma-w.
+;;; delta-w = gamma-w·sigma-w.
 
 ;;; We will use encapsulate for that purpose. Let sigma-w, delta-w and
 ;;; gamma-w three susbtitutions such that delta-w is functionally equal
Index: acl2-8.4dfsg/books/defexec/dag-unification/subsumption.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/subsumption.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/subsumption.lisp
@@ -1,7 +1,7 @@
 ;;; subsumption.lisp Definition of a particular RULE-BASED matching
 ;;; algorithm between terms.  We use functional instantion of the
 ;;; pattern given in matching.lisp Using this algorithm, we define the
-;;; subsumption relation between terms and lists of terms in a
+;;; subsumption relńation between terms and lists of terms in a
 ;;; constructive way, and we prove that subsumption is a preorder.
 ;;; Created: 11-10-99 Last revison: 07-12-2000
 ;;; =============================================================================
@@ -287,7 +287,7 @@
 ;;; Most of these properties are obtained by functional instantiation.
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 (defthm subs-soundness
   (implies (subs t1 t2)
@@ -298,7 +298,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ·············
 
 (defthm subs-completeness
   (implies (equal (instance t1 sigma) t2)
@@ -308,7 +308,7 @@
 	   (:instance match-mv-completeness (S (list (cons t1 t2)))))))
 
 ;;; Substitution-s-p (closure property)
-;;; 
+;;; ···································
 
 
 (defthm matching-substitution-s-p
@@ -318,7 +318,7 @@
 	   (:instance match-mv-substitution-s-p (S (list (cons t1 t2)))))))
 
 ;;; Substitution-p (needed for guard verification)
-;;; 
+;;; ··············································
 
 
 (defthm matching-substitution-p
@@ -409,7 +409,7 @@
    (second (pair-args l1 (apply-subst nil sigma l1)))))
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 
 (defthm subs-list-soundness
@@ -421,7 +421,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ·············
 
 (defthm subs-list-completeness
   (implies (equal (apply-subst nil sigma l1) l2)
@@ -431,7 +431,7 @@
 	   (:instance match-mv-completeness (S (first (pair-args l1 l2)))))))
 
 ;;; Substitution-s-p (closure property)
-;;; 
+;;; ···································
 
 
 (defthm matching-list-substitution-s-p
@@ -444,7 +444,7 @@
 
 
 ;;; Substitution-p (needed for guard verification)
-;;; 
+;;; ··············································
 
 
 (defthm matching-list-substitution-p
@@ -498,7 +498,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;;; Subsumption reflexive
-;;;; 
+;;;; ·····················
 
 (defthm subsumption-reflexive
    (subs t1 t1)
@@ -508,7 +508,7 @@
 
 
 ;;;; Subsumption transitive
-;;;; 
+;;;; ······················
 
 
 (defthm subsumption-transitive
@@ -528,7 +528,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;; An useful rule:
-;;; 
+;;; ···············
 
 (defthm subsumption-apply-subst
   (subs term (instance term sigma))
@@ -536,7 +536,7 @@
 				  (t1 term) (t2 (instance term sigma))))))
 
 ;;; Variables are minimum elements in this quasi-order
-;;; 
+;;; ··················································
 
 (defthm variable-minimum-subsumption
   (implies (variable-p x)
Index: acl2-8.4dfsg/books/defexec/dag-unification/terms-as-dag.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/terms-as-dag.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/terms-as-dag.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; terms-as-dag.lisp
-;;; Ttulo: Storing first--order terms as dags
+;;; Título: Storing first--order terms as dags
 ;;; ============================================================================
 
 #| To certify this book:
@@ -20,7 +20,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
Index: acl2-8.4dfsg/books/defexec/dag-unification/terms-dag-stobj.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/terms-dag-stobj.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/terms-dag-stobj.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; terms-dag-stobj.lisp
-;;; Ttulo: The single--threaded object {\tt terms-dag}
+;;; Título: The single--threaded object {\tt terms-dag}
 ;;; ============================================================================
 
 #| To certify this book:
@@ -16,7 +16,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
Index: acl2-8.4dfsg/books/defexec/dag-unification/terms.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/defexec/dag-unification/terms.lisp
+++ acl2-8.4dfsg/books/defexec/dag-unification/terms.lisp
@@ -939,7 +939,7 @@
        (disjointp (variables nil (co-domain S)) (domain S))))
 
 ;;; REMARK: In the literature, idempotent substitutions are defined as
-;;; substitutions sigma such that sigmasigma = sigma. But this
+;;; substitutions sigma such that sigma·sigma = sigma. But this
 ;;; definition involves functional equality. We will see that the above
 ;;; definition implies this property (see main-property-mgs in the book
 ;;; unification-definition.lisp) Nevertheless, the definition does not
@@ -949,9 +949,9 @@
 ;;; functionally equivalent idempotent (in our sense) substitution, ((x
 ;;; . y)) in this case.
 
-;;; 
+;;; ············································································
 ;;; 3.3.1 The main property of idempotent substitutions.
-;;; 
+;;; ············································································
 
 ;;; .... PROOF PLAN:
 
@@ -1103,9 +1103,9 @@
 ;;; 4.2 Some results concerning the tree structure of a term
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ············································································
 ;;; 4.2.1 Concatenation of positions
-;;; 
+;;; ············································································
 
 (defthm position-p-append
   (implies (position-p p1 term)
@@ -1128,9 +1128,9 @@
 					      q x)))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.2 Substitutions and positions
-;;; 
+;;; ············································································
 
 (defthm nth-apply-subst
   (implies (and (integerp i)
@@ -1165,9 +1165,9 @@
 	    (instance (replace-term term pos t1) sigma))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.3 Prefix positions
-;;; 
+;;; ············································································
 
 (local
  (defthm equal-len-replace-list
@@ -1202,9 +1202,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.4 Disjoint positions
-;;; 
+;;; ············································································
 
 (local
  (defun induct-position-p-disjoint (pos1 pos2 term)
@@ -1267,9 +1267,9 @@
 			   (position-p (cons i pos) (cons fn args)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.5 Disabling the theory
-;;; 
+;;; ············································································
 
 (defconst *tree-structure-of-terms*
   '(position-p-append occurrence-append replace-term-append
Index: acl2-8.4dfsg/books/workshops/2000/medina/polynomials/README
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/medina/polynomials/README
+++ acl2-8.4dfsg/books/workshops/2000/medina/polynomials/README
@@ -19,6 +19,6 @@ http://www-cs.us.es/~imedina/polynomials
 
 and in the following paper:
 
-Medina-Bulo, I; Alonso-Jimnez, J. A. & Palomo-Lozano, F.
+Medina-Bulo, I; Alonso-Jiménez, J. A. & Palomo-Lozano, F.
 Automatic Verification of Polynomial Rings Fundamental Properties in ACL2
 ACL2 Workshop 2000.
Index: acl2-8.4dfsg/books/workshops/2000/medina/polynomials/polynomial.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/medina/polynomials/polynomial.lisp
+++ acl2-8.4dfsg/books/workshops/2000/medina/polynomials/polynomial.lisp
@@ -6,7 +6,7 @@
 ;;; Polynomial recognizer
 ;;; ---------------------
 
-;;; Similar to integer-listp function.
+;;; Similar to «integer-listp» function.
 
 (defun monomial-listp (l)
   (cond ((atom l)
Index: acl2-8.4dfsg/books/workshops/2000/medina/polynomials/term.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/medina/polynomials/term.lisp
+++ acl2-8.4dfsg/books/workshops/2000/medina/polynomials/term.lisp
@@ -4,7 +4,7 @@
 ;;; Natural recognizer
 ;;; ------------------
 
-;;; Similar to integerp macro.
+;;; Similar to «integerp» macro.
 
 (defmacro naturalp (x)
   `(and (integerp ,x) (COMMON-LISP::<= 0 ,x)))
@@ -13,7 +13,7 @@
 ;;; True list of naturals recognizer
 ;;; --------------------------------
 
-;;; Similar to integer-listp function.
+;;; Similar to «integer-listp» function.
 
 (defun natural-listp (l)
   (cond ((atom l)
Index: acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/ackermann/ackermann.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/ruiz/multiset/examples/ackermann/ackermann.lisp
+++ acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/ackermann/ackermann.lisp
@@ -25,7 +25,7 @@
 ;;; ===========================================================================
 
 ;;; This is the Ackermann function, classical definition:
-;;; 
+;;; ·····················································
 
 (defun ack (m n)
   (declare (xargs :measure (cons (+ (nfix m) 1) (nfix n))
@@ -44,7 +44,7 @@
 (verify-guards ack)
 
 ;;; Our goal is to define an iterative version of ack:
-;;; 
+;;; ··················································
 
 ; (defun ack-it-aux (s z)
 ;   (declare (xargs :mode :program))
@@ -136,7 +136,7 @@
 ;;;----------------------------------------------------------------------------
 
 ;;; Some lemmas needed to the admission of ack-it-aux
-;;; 
+;;; ·················································
 
 ;;; 1)
 
@@ -192,7 +192,7 @@
 
 
 ;;; At last, admission of ack-it-aux and definition of ack-it
-;;; 
+;;; ·························································
 
 (defun nn-integer-true-listp (s)
   (declare (xargs :guard t))
Index: acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/newman/confluence-v0.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/ruiz/multiset/examples/newman/confluence-v0.lisp
+++ acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/newman/confluence-v0.lisp
@@ -327,9 +327,9 @@
 (defun provably-equivalent (x y)
   (equal (normal-form x) (normal-form y)))
 
-;;; 
+;;; ············································································
 ;;; 2.2.1 Completeness
-;;; 
+;;; ············································································
 
 ;;; A proof between normal forms
 (local
@@ -386,9 +386,9 @@
 			 (p (make-proof-between-normal-forms x y p)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.2.1 Soundness
-;;; 
+;;; ············································································
 
 ;;; A proof between x and y (if their normal forms are equal)
 
Index: acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/newman/confluence.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/ruiz/multiset/examples/newman/confluence.lisp
+++ acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/newman/confluence.lisp
@@ -305,9 +305,9 @@
 (defun r-equiv (x y)
   (equal (normal-form x) (normal-form y)))
 
-;;; 
+;;; ············································································
 ;;; 2.2.1 Completeness
-;;; 
+;;; ············································································
 
 ;;; A proof between normal forms
 (local
@@ -364,9 +364,9 @@
 			 (p (make-proof-between-normal-forms x y p)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.2.1 Soundness
-;;; 
+;;; ············································································
 
 ;;; A proof between x and y (if their normal forms are equal)
 
Index: acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/newman/local-confluence.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/ruiz/multiset/examples/newman/local-confluence.lisp
+++ acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/newman/local-confluence.lisp
@@ -159,7 +159,7 @@
 
 
 ;;; A noetherian and locally confluent reduction relation
-;;; 
+;;; ·····················································
 
 
 (encapsulate
@@ -227,7 +227,7 @@
 ;;; See newman.lisp for details.
 
 ;;; Well-founded multiset extension of rel
-;;; 
+;;; ······································
 
 ;(acl2::defmul-components rel)
 ;The list of components is:
@@ -237,7 +237,7 @@
 
 
 ;;; Auxiliary functions in the definition of transform-to-valley
-;;; 
+;;; ···························································
 
 (local
  (defun exists-local-peak (p)
@@ -260,7 +260,7 @@
 
 
 ;;; transform-to-valley terminates
-;;; 
+;;; ······························
 
 ;;; By functional instantiation of the same result in newman.lisp
 
@@ -283,7 +283,7 @@
 
 
 ;;; Definition of transform-to-valley
-;;; 
+;;; ·································
 
 (local
  (defun transform-to-valley (p)
@@ -298,7 +298,7 @@
 
 
 ;;; Properties of transform-to-valley: the Church-Rosser property
-;;; 
+;;; ·····························································
 
 ;;; By functional instantiation of the same results in newman.lisp
 
@@ -338,7 +338,7 @@
 ;;; axioms.
 
 ;;; Definition of proof-irreducible
-;;; 
+;;; ·······························
 
 ;;; REMARK: Iteratively apply reduction steps until an irreducible
 ;;; element is found. This function termination can be justified by the
@@ -358,7 +358,7 @@
 
 
 ;;; Properties of proof-irreducible (normalizing property)
-;;; 
+;;; ······················································
 
 ;;; REMARK: These are the assumed proerties of proof-irreducible in
 ;;; confluence.lisp, in rewriting rule form:
@@ -404,7 +404,7 @@
 
 
 ;;; This is the same function as r-equiv in confluence.lisp
-;;; 
+;;; ·······················································
 
 ;;; REMARK: normal-form-aux is analogue NWM::normal-form, but
 ;;; normal-form is more eficcient. The same for r-equiv.
@@ -428,7 +428,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;; Completeness
-;;; 
+;;; ············
 
 ;;; By functional instantiation of the same results in confluence.lisp
 
@@ -448,7 +448,7 @@
 
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 ;;; By functional instantiation of the same results in confluence.lisp
 
Index: acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/newman/newman.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/ruiz/multiset/examples/newman/newman.lisp
+++ acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/examples/newman/newman.lisp
@@ -322,9 +322,9 @@
 
 ;;; In the sequel, we build a collection of rules to prove these two goals.
 
-;;; 
+;;; ············································································
 ;;; 3.2.1 Removing initial and final common parts
-;;; 
+;;; ············································································
 
 
 (local
@@ -396,9 +396,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 3.2.2 Removing the first element of the local peak
-;;; 
+;;; ············································································
 
 ;;; First, let's prove that the local peak and the transformed are
 ;;; proofs with the same endpoints, so their proof measures have the
@@ -533,12 +533,12 @@
 ;;;         (CDR (PROOF-MEASURE (TRANSFORM-LOCAL-PEAK (LOCAL-PEAK P))))))).
 
 
-;;; 
+;;; ············································································
 ;;; 3.2.3 An explicit reference to the peak-element
-;;; 
+;;; ············································································
 
 ;;; Definition and properties of peak-element
-;;; 
+;;; ·········································
 
 ;;; See the definition in abstract-proofs.lisp
 
@@ -592,13 +592,13 @@
 ;;;           (CDR (PROOF-MEASURE (TRANSFORM-LOCAL-PEAK (LOCAL-PEAK P))))))).
 
 
-;;; 
+;;; ············································································
 ;;; 3.2.4 The peak element is bigger than any element of
 ;;; (transform-local-peak (local-peak p))
-;;; 
+;;; ············································································
 
 ;;; Definition of being bigger (w.r.t rel) than every element of a list
-;;; 
+;;; ···································································
 
 (local
  (defun rel-bigger-than-list (x l)
@@ -610,7 +610,7 @@
 ;;; Conditions assuring that an element m is rel-bigger-than-list than
 ;;; the elements of the proof-measure of a proof, when the proof is,
 ;;; respectively, steps-up or steps-down:
-;;; 
+;;; ···································································
 
 ;;; A previous lemma: transitivity of rel is needed here
 
@@ -653,7 +653,7 @@
 ;;; (transform-local-peak (local-peak p)) in two proofs: the proof
 ;;; before the valley (steps-up) and the proof after the valley
 ;;; (steps-down). The following lemmas are needed for that purpose.
-;;; 
+;;; ····································································
 
 ;;; If p is a proof, so they are the proofs after and before the
 ;;; valley.
@@ -682,7 +682,7 @@
 
 
 ;;; The transformed proof is a valley
-;;; 
+;;; ·································
 
 (local
  (defthm local-peak-local-peak-p
@@ -707,7 +707,7 @@
 ;;; steps-up-proof-measure-w-f-v (and then prove that the peak-element
 ;;; is bigger than every element of the complexities of the
 ;;; proof-after-valley and the proof-before-valley, respectively.
-;;; 
+;;; ····································································
 
 
 
@@ -734,7 +734,7 @@
 
 
 ;;; Some technical lemmas
-;;; 
+;;; ·····················
 
 (local
  (defthm consp-proof-after-proof-instance
@@ -750,7 +750,7 @@
 
 
 ;;; And finally, the intended lemma
-;;; 
+;;; ·······························
 
 (local
  (defthm valley-rel-bigger-peak-lemma
@@ -763,9 +763,9 @@
                                     (transform-local-peak (local-peak p))))))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.2.5 Using valley-rel-bigger-peak-lemma to simplify the goals
-;;; 
+;;; ············································································
 
 ;;; The two unresolved goals, as stated at the end of 3.2.3, can be
 ;;; simplified to t by using the previously proved
@@ -776,7 +776,7 @@
 ;;; following lemma (stating that the peak-element is not a member of
 ;;; the proof-meassure of the transformed proof),
 ;;; the calls to multiset-diff in the goals now disappear.
-;;; 
+;;; ···································································
 
 (local
  (encapsulate
@@ -813,7 +813,7 @@
 ;;; in the unresolved goal above, is reduced to a call to
 ;;; rel-bigger-than-list (and then valley-rel-bigger-peak-lemma will be
 ;;; applied)
-;;; 
+;;; ···································································
 
 
 (local
@@ -830,9 +830,9 @@
 ;;; With this two rules altogether with valley-rel-bigger-peak-lemma our
 ;;; unresolved goal becomes T, so we have:
 
-;;; 
+;;; ············································································
 ;;; 3.2.6  The main lemma of this book
-;;; 
+;;; ············································································
 
 (defthm transform-to-valley-admission
   (implies (exists-local-peak p)
@@ -866,13 +866,13 @@
 ;;; 4.1 Some previous events
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ·············································································
 ;;; 4.1.1 Previous rules needed to show that (transform-to-valley p) is eqv. to p
-;;; 
+;;; ·············································································
 
 
 ;;; We have to see that (replace-local-peak p) is equivalent to p
-;;; 
+;;; ··································································
 
 ;;; An useful rule to deal with concatenation of proofs
 (local
@@ -936,9 +936,9 @@
 ;;; three pieces of p (before, at and after the peak), using the
 ;;; previous bridge lemma.
 
-;;; 
+;;; ·············································································
 ;;; 4.1.2 A rule needed to show that (transform-to-valley p) is a valley
-;;; 
+;;; ·············································································
 
 
 
@@ -950,9 +950,9 @@
             (equal  (steps-valley p) (not (exists-local-peak p))))))
 
 
-;;; 
+;;; ·············································································
 ;;; 4.1.3 Disabling the induction rule for equiv-p
-;;; 
+;;; ·············································································
 
 
 (local (in-theory (disable equiv-p-induct)))
@@ -969,7 +969,7 @@
 
 
 ;;; It returns an equivalent proof
-;;; 
+;;; ······························
 
 
 (defthm equiv-p-x-y-transform-to-valley
@@ -980,7 +980,7 @@
 
 
 ;;; It returns a valley proof
-;;; 
+;;; ·························
 
 
 (defthm valley-transform-to-valley
Index: acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/multiset.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2000/ruiz/multiset/multiset.lisp
+++ acl2-8.4dfsg/books/workshops/2000/ruiz/multiset/multiset.lisp
@@ -559,9 +559,9 @@
 ;;;    (e0-ord-< (map-fn-e0-ord n) (map-fn-e0-ord m))
 
 
-;;; 
+;;; ············································································
 ;;; 2.5.1 The measure is an ordinal.
-;;; 
+;;; ············································································
 
 (local
  (defthm e0-ordinalp-insert-e0-ord-<
@@ -577,9 +577,9 @@
 	    (e0-ordinalp (map-fn-e0-ord m)))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.5.2 The measure is an embedding
-;;; 
+;;; ············································································
 
 
 
@@ -613,7 +613,7 @@
 
 
 ;;; max-fn1-list (an element in l with maximal (fn1 ..)) and properties.
-;;; 
+;;; ······································································
 
 (local
  (defun max-fn1-list (l)
@@ -652,7 +652,7 @@
 
 
 ;;; An "alternative definition" of "map-fn-e0-ord".
-;;; 
+;;; ···············································
 
 (local
  (encapsulate
@@ -786,7 +786,7 @@
 
 
 ;;; Needed for forall-exists-rel-bigger-max-fn1-list
-;;; 
+;;; ················································
 
 ;;; We prove forall-exists-rel-bigger-max-fn1-list-lemma, establishing
 ;;; that if (mul-rel n m), and x is in n and not in m, then (fn1 x) is
@@ -882,7 +882,7 @@
 
 
 ;;; Previous lemmas to map-fn-e0-ord-measure, handling every subgoal
-;;; 
+;;; ································································
 
 ;;; Needed for "Subgoal *1/8":
 
@@ -964,7 +964,7 @@
 
 
 ;;; At last: map-fn-e0-ord-measure.
-;;; 
+;;; ·······························
 
 (local
  (encapsulate
Index: acl2-8.4dfsg/books/workshops/2002/medina-palomo-alonso/support/section-2/README
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/medina-palomo-alonso/support/section-2/README
+++ acl2-8.4dfsg/books/workshops/2002/medina-palomo-alonso/support/section-2/README
@@ -34,7 +34,7 @@ Encapsulated events, with the exception
 their corresponding congruences, are developed in (event names may
 have changed):
 
-[1] Medina Bulo, I., Alonso Jimnez, J. A., Palomo Lozano, F.:
+[1] Medina Bulo, I., Alonso Jiménez, J. A., Palomo Lozano, F.:
     Automatic Verification of Polynomial Rings Fundamental Properties in ACL2.  
     The University of Texas at Austin, Department of Computer Sciences.	
     Technical Report 0029 (2000)
Index: acl2-8.4dfsg/books/workshops/2002/medina-palomo-alonso/support/section-3/README
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/medina-palomo-alonso/support/section-3/README
+++ acl2-8.4dfsg/books/workshops/2002/medina-palomo-alonso/support/section-3/README
@@ -53,7 +53,7 @@ orderings.
 
 Encapsulated events are developed in (event names may have changed):
 
-[1] Medina Bulo, I., Alonso Jimnez, J. A., Palomo Lozano, F.:
+[1] Medina Bulo, I., Alonso Jiménez, J. A., Palomo Lozano, F.:
     Automatic Verification of Polynomial Rings Fundamental Properties in ACL2.  
     The University of Texas at Austin, Department of Computer Sciences.	
     Technical Report 0029 (2000)
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-dags/support/dags.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-dags/support/dags.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-dags/support/dags.lisp
@@ -498,7 +498,7 @@
        (not (dag-p-aux hs rp g))))
 
 ;;; Finally, the soundness theorem:
-;;; 
+;;; ·······························
 
 (defthm dag-p-soundness
   (implies (not (dag-p g))
@@ -542,7 +542,7 @@
 
 
 ;;; The main lemma for completeness:
-;;; 
+;;; ································
 
 (local
  (defthm dag-p-aux-completeness-main-lemma
@@ -642,7 +642,7 @@
 
 
 ;; Finally, the completeness theorem:
-;;; 
+;;; ··································
 
 
  (defthm dag-p-completeness
@@ -1106,7 +1106,7 @@
 
 
 ;;; RECALL: These two theorems would allow us to define functions like these:
-;;; 
+;;; ·········································································
 
 
 ; (defun occur-check-l (flg x h g)
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-dags/support/terms.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-dags/support/terms.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-dags/support/terms.lisp
@@ -928,7 +928,7 @@
        (disjointp (variables nil (co-domain S)) (domain S))))
 
 ;;; REMARK: In the literature, idempotent substitutions are defined as
-;;; substitutions sigma such that sigmasigma = sigma. But this
+;;; substitutions sigma such that sigma·sigma = sigma. But this
 ;;; definition involves functional equality. We will see that the above
 ;;; definition implies this property (see main-property-mgs in the book
 ;;; unification-definition.lisp) Nevertheless, the definition does not
@@ -938,9 +938,9 @@
 ;;; functionally equivalent idempotent (in our sense) substitution, ((x
 ;;; . y)) in this case.
 
-;;; 
+;;; ············································································
 ;;; 3.3.1 The main property of idempotent substitutions.
-;;; 
+;;; ············································································
 
 ;;; .... PROOF PLAN:
 
@@ -1092,9 +1092,9 @@
 ;;; 4.2 Some results concerning the tree structure of a term
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ············································································
 ;;; 4.2.1 Concatenation of positions
-;;; 
+;;; ············································································
 
 (defthm position-p-append
   (implies (position-p p1 term)
@@ -1117,9 +1117,9 @@
 					      q x)))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.2 Substitutions and positions
-;;; 
+;;; ············································································
 
 (defthm nth-apply-subst
   (implies (and (integerp i)
@@ -1154,9 +1154,9 @@
 	    (instance (replace-term term pos t1) sigma))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.3 Prefix positions
-;;; 
+;;; ············································································
 
 (local
  (defthm equal-len-replace-list
@@ -1191,9 +1191,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.4 Disjoint positions
-;;; 
+;;; ············································································
 
 (local
  (defun induct-position-p-disjoint (pos1 pos2 term)
@@ -1256,9 +1256,9 @@
 			   (position-p (cons i pos) (cons fn args)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.5 Disabling the theory
-;;; 
+;;; ············································································
 
 (defconst *tree-structure-of-terms*
   '(position-p-append occurrence-append replace-term-append
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/anti-unification.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/anti-unification.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/anti-unification.lisp
@@ -206,9 +206,9 @@
 ;;; (pre-anti-unify-aux flg t1 t2 phi) computes a glb of t1 and t2,
 ;;; whenever it exists.
 
-;;; 
+;;; ············································································
 ;;; 2.2.1 Assumptions on phi
-;;; 
+;;; ············································································
 
 ;;; The following function defines the properties we are going to
 ;;; assume about an injection phi: it has to be an association such that
@@ -232,9 +232,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 2.2.2 pre-anti-unify-aux computes a generalization of t1 and t2
-;;; 
+;;; ············································································
 
 ;;; We have to prove something like:
 ;  (let* ((glb (pre-anti-unify-aux flg t1 t2 phi))
@@ -449,10 +449,10 @@
 	     (equal (apply-subst flg sigma (first glb)) t2)))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.2.3 pre-anti-unify-aux computes the least common generalization of
 ;;; t1 and t2
-;;; 
+;;; ············································································
 
 ;;; This means, using completeness, that we have to construct, given an
 ;;; lower bound of t1 and t2, term, a matching substitution for term and
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/matching.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/matching.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/matching.lisp
@@ -89,9 +89,9 @@
 ;;; ----------------------------------------------------------------------------
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.1 How we deal with selection.
-;;; 
+;;; ············································································
 
 
 ;;; Firs we prove that equal-set is a congruence w.r.t. the second
@@ -139,9 +139,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.2 transform-subs-sel preserves the set of matchers.
-;;; 
+;;; ············································································
 
 
 (local
@@ -211,7 +211,7 @@
 	      (not (matcher sigma S)))))
 
 ;;; The three main theorems of this subsubsection
-;;; 
+;;; ·············································
 
   (defthm transform-subs-sel-preserves-matchers-1
     (implies
@@ -235,10 +235,10 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.3 (system-substitution (cdr S-match)) is an invariant in the rules
 ;;;     of transformation.
-;;; 
+;;; ············································································
 
 
 
@@ -261,9 +261,9 @@
      (system-substitution (cdr (transform-subs-sel S-match)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.4 Main property of the property system-substitution
-;;; 
+;;; ············································································
 
 
 (local
@@ -360,7 +360,7 @@
 			(length-term nil args2))))))
 
 ;;; And the main result:
-;;; 
+;;; ····················
 
   (defthm transform-subs-sel-decreases-length-of-first-system
     (implies (not (normal-form-syst S-match))
@@ -458,7 +458,7 @@
 
 ;;; Three lemmas to state that the set of matchers is preserved by
 ;;; subs-system-sel
-;;; 
+;;; ··········································································
 
 (local
  (defthm subs-system-sel-preserves-matchers-1
@@ -486,7 +486,7 @@
 (in-theory (enable union-systems))
 
 ;;; subs-system-sel preserves the property of being a system-substitution.
-;;; 
+;;; ··································································
 
 (local
  (defthm subs-system-sel-preserves-system-substitution
@@ -494,7 +494,7 @@
 	   (system-substitution (cdr (subs-system-sel S-match))))))
 
 ;;; Guard verification: a substitution-s-p is returned
-;;; 
+;;; ···················································
 
 (local
  (defthm
@@ -602,7 +602,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 
 (defthm subs-sel-soundness
@@ -616,7 +616,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ············
 
 
 (defthm subs-sel-completeness
@@ -630,7 +630,7 @@
 
 ;;; Closure property:
 ;;; (the following theorem is needed for guard verification)
-;;; 
+;;; ························································
 
 
 (defthm matching-sel-substitution-s-p
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/renamings.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/renamings.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/renamings.lisp
@@ -101,9 +101,9 @@
 ;;; ----------------------------------------------------------------------------
 
 
-;;; 
+;;; ············································································
 ;;; 2.2.1 An important lemma
-;;; 
+;;; ············································································
 
 ;;; We will show that the inverse substitution of a renaming is its
 ;;; inverse function, in some sense.
@@ -145,9 +145,9 @@
 	      term))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.2.2 And the intended property
-;;; 
+;;; ············································································
 
 
 (defthm renaming-implies-renamed
@@ -180,9 +180,9 @@
 ;;;  * (co-domain sigmar) is a setp.
 
 
-;;; 
+;;; ············································································
 ;;; 2.3.1 sigmar is a variable-substitution
-;;; 
+;;; ············································································
 
 (local
  (encapsulate
@@ -222,9 +222,9 @@
 	     (:instance renamed-implies-variable-substitution-main-lemma
 			(l (make-set (variables flg term)))))))))
 
-;;; 
+;;; ············································································
 ;;; 2.3.2 An important lemma
-;;; 
+;;; ············································································
 
 ;;; When (equal (apply-subst flg delta (apply-subst flg sigma term))
 ;;; term) then two different variables of term cannot have the the value
@@ -267,9 +267,9 @@
 				     (x y))))))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.3.2 co-domain of sigmar is a setp
-;;; 
+;;; ············································································
 
 
 
@@ -298,9 +298,9 @@
 	     (:instance renamed-implies-setp-codomain-main-lemma
 			(l (make-set (variables flg term)))))))))
 
-;;; 
+;;; ············································································
 ;;; 2.3.3 sigmar is a renaming
-;;; 
+;;; ············································································
 
 (local
  (defthm renamed-implies-renaming-main-lemma
@@ -436,9 +436,9 @@
 ;;; 3.3 Number-rename-aux: main properties.
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ············································································
 ;;; 3.3.1 Previous (local) lemmas about coincide.
-;;; 
+;;; ············································································
 
 ;;; We will need these lemmas because we are going to talk about
 ;;; extensions (see the definition in terms.lisp, subsection 2.3)
@@ -483,9 +483,9 @@
   (in-theory (disable coincide-subsetp-transitive))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.3.2 Previous (local) lemmas about acl2-numberp-list-increment
-;;; 
+;;; ············································································
 
 ;;; We will define and prove some local properties of the concept of
 ;;; being a list of numbers l such that each of its elements is obtained
@@ -542,9 +542,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 3.3.3 number-rename-aux: properties of the variables of the returned term
-;;; 
+;;; ············································································
 
 ;;; We will prove that (first (number-rename-aux flg term sigma x y) is a
 ;;; term having numeric variables, and:
@@ -611,10 +611,10 @@
 		(second (number-rename-aux flg term sigma x y))) x))))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.3.4 number-rename-aux: Main property of the co-domain of the
 ;;; returned substitution.
-;;; 
+;;; ············································································
 
 
 (local
@@ -625,9 +625,9 @@
 	    (acl2-numberp-list-increment
 	     (co-domain (second (number-rename-aux flg term sigma x y))) y))))
 
-;;; 
+;;; ············································································
 ;;; 3.3.5 number-rename-aux: the substitution returned is a renaming
-;;; 
+;;; ············································································
 
 
 (local
@@ -659,16 +659,16 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 3.3.3 Subsumption properties of number-rename-aux
-;;; 
+;;; ············································································
 
 
 ;;; 3.3.3.1
 ;;; The substituion returned by  number-rename-aux, applied to the input
 ;;; term returns the returned term (i.e term subsumes the
 ;;; number-rename-aux term)
-;;; 
+;;; ··········································································
 
 ;;; Two previos lemmas:
 
@@ -735,7 +735,7 @@
 
 ;;; 3.3.3.2
 ;;; The term returned by number-rename-aux subsumes the input term
-;;; 
+;;; ···································································
 
 (local
  (encapsulate
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/subsumption-subst.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/subsumption-subst.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/subsumption-subst.lisp
@@ -26,15 +26,15 @@
 ;;; Our goal is to define the subsumption relation between
 ;;; substitutions. In the literature, this relation is defined in this
 ;;; way:
-;;;     sigma <= delta iff (exists gamma) gammasigma = delta
-;;; where "" stands for composition.
+;;;     sigma <= delta iff (exists gamma) gamma·sigma = delta
+;;; where "·" stands for composition.
 
 ;;; Note that equality between substitutions is functional equality (we cannot
 ;;; use equal), so we reformulate this property as:
 
 ;;; (*) sigma <= delta iff (exists gamma)
 ;;;                        s.t. for all term
-;;;                        gammasigma(term) = delta(term)
+;;;                        gamma·sigma(term) = delta(term)
 
 
 ;;; Our goal in this book is to define the subsumption relation between
@@ -285,9 +285,9 @@
 ;;; if (subs-sust sigma delta)
 ;;; WE DISTINGUISH THREE CASES.
 
-;;; 
+;;; ············································································
 ;;; 3.1.1 Case 1: x is a variable outside V
-;;; 
+;;; ············································································
 
 
 
@@ -303,14 +303,14 @@
    :hints (("Goal" :in-theory (enable x-not-in-domain-remains-the-same)))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.1.2. Case 2: x is a variable of (domain-var sigma)
-;;; 
+;;; ············································································
 
 
 ;;; 3.1.2.1 A lemma for this case 2:
 ;;; subs-subst composed with sigma is equal to delta in V.
-;;; 
+;;; ······················································
 
 (local
  (encapsulate
@@ -373,7 +373,7 @@
 (local (in-theory (disable subs-subst matching-subst)))
 
 ;;; 3.1.2.2 Another lemma for case 2:
-;;; 
+;;; ·······························
 
 (local
  (defthm variables-co-domain-var
@@ -383,7 +383,7 @@
 
 
 ;;; 3.1.2.3 The main result for Case 2
-;;; 
+;;; ································
 
 (local
  (defthm
@@ -396,14 +396,14 @@
 		   (val x delta)))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.1.3. Case 3: x in V but not in (domain-var sigma)
-;;; 
+;;; ············································································
 
 
 ;;; 3.1.3.1 A lemma for Case 3
 ;;; In this case, matching and matching-subst-r take the same values.
-;;; 
+;;; ·································································
 
 (local
  (defthm
@@ -472,7 +472,7 @@
 
 
 ;;; With terms and list of terms (not only with variables)
-;;; 
+;;; ······················································
 
 (local
  (defthm
@@ -512,7 +512,7 @@
 ;;; following version will be used as a rewrite rule.
 
 ;;; With terms but without using composition
-;;; 
+;;; ········································
 
 (defthm
   subs-subst-implies-matching-subst-r-appplied-to-sigma-term-is-delta-term
@@ -526,7 +526,7 @@
 
 
 ;;; With respect to subsumption between terms
-;;; 
+;;; ·········································
 
 
 ;;; Trivial consequence of completeness of subsumption and the previous
@@ -563,7 +563,7 @@
 ;;; existence of two substitutions, called sigma-w and delta-w and the
 ;;; only property we will assume about them is that sigma-w <=
 ;;; delta-w. That is, exists another substitution gamma-w such that
-;;; delta-w = gamma-wsigma-w.
+;;; delta-w = gamma-w·sigma-w.
 
 ;;; We will use encapsulate for that purpose. Let sigma-w, delta-w and
 ;;; gamma-w three susbtitutions such that delta-w is functionally equal
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/subsumption.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/subsumption.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/subsumption.lisp
@@ -289,7 +289,7 @@
 ;;; Most of these properties are obtained by functional instantiation.
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 (defthm subs-soundness
   (implies (subs t1 t2)
@@ -300,7 +300,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ·············
 
 (defthm subs-completeness
   (implies (equal (instance t1 sigma) t2)
@@ -310,7 +310,7 @@
 	   (:instance match-mv-completeness (S (list (cons t1 t2)))))))
 
 ;;; Substitution-s-p (closure property)
-;;; 
+;;; ···································
 
 
 (defthm matching-substitution-s-p
@@ -320,7 +320,7 @@
 	   (:instance match-mv-substitution-s-p (S (list (cons t1 t2)))))))
 
 ;;; Substitution-p (needed for guard verification)
-;;; 
+;;; ··············································
 
 
 (defthm matching-substitution-p
@@ -411,7 +411,7 @@
    (second (pair-args l1 (apply-subst nil sigma l1)))))
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 
 (defthm subs-list-soundness
@@ -423,7 +423,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ·············
 
 (defthm subs-list-completeness
   (implies (equal (apply-subst nil sigma l1) l2)
@@ -433,7 +433,7 @@
 	   (:instance match-mv-completeness (S (first (pair-args l1 l2)))))))
 
 ;;; Substitution-s-p (closure property)
-;;; 
+;;; ···································
 
 
 (defthm matching-list-substitution-s-p
@@ -446,7 +446,7 @@
 
 
 ;;; Substitution-p (needed for guard verification)
-;;; 
+;;; ··············································
 
 
 (defthm matching-list-substitution-p
@@ -500,7 +500,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;;; Subsumption reflexive
-;;;; 
+;;;; ·····················
 
 (defthm subsumption-reflexive
    (subs t1 t1)
@@ -510,7 +510,7 @@
 
 
 ;;;; Subsumption transitive
-;;;; 
+;;;; ······················
 
 
 (defthm subsumption-transitive
@@ -530,7 +530,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;; An useful rule:
-;;; 
+;;; ···············
 
 (defthm subsumption-apply-subst
   (subs term (instance term sigma))
@@ -538,7 +538,7 @@
 				  (t1 term) (t2 (instance term sigma))))))
 
 ;;; Variables are minimum elements in this quasi-order
-;;; 
+;;; ··················································
 
 (defthm variable-minimum-subsumption
   (implies (variable-p x)
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/terms.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/terms.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/terms.lisp
@@ -927,7 +927,7 @@
        (disjointp (variables nil (co-domain S)) (domain S))))
 
 ;;; REMARK: In the literature, idempotent substitutions are defined as
-;;; substitutions sigma such that sigmasigma = sigma. But this
+;;; substitutions sigma such that sigma·sigma = sigma. But this
 ;;; definition involves functional equality. We will see that the above
 ;;; definition implies this property (see main-property-mgs in the book
 ;;; unification-definition.lisp) Nevertheless, the definition does not
@@ -937,9 +937,9 @@
 ;;; functionally equivalent idempotent (in our sense) substitution, ((x
 ;;; . y)) in this case.
 
-;;; 
+;;; ············································································
 ;;; 3.3.1 The main property of idempotent substitutions.
-;;; 
+;;; ············································································
 
 ;;; .... PROOF PLAN:
 
@@ -1091,9 +1091,9 @@
 ;;; 4.2 Some results concerning the tree structure of a term
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ············································································
 ;;; 4.2.1 Concatenation of positions
-;;; 
+;;; ············································································
 
 (defthm position-p-append
   (implies (position-p p1 term)
@@ -1116,9 +1116,9 @@
 					      q x)))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.2 Substitutions and positions
-;;; 
+;;; ············································································
 
 (defthm nth-apply-subst
   (implies (and (integerp i)
@@ -1153,9 +1153,9 @@
 	    (instance (replace-term term pos t1) sigma))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.3 Prefix positions
-;;; 
+;;; ············································································
 
 (local
  (defthm equal-len-replace-list
@@ -1190,9 +1190,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.4 Disjoint positions
-;;; 
+;;; ············································································
 
 (local
  (defun induct-position-p-disjoint (pos1 pos2 term)
@@ -1255,9 +1255,9 @@
 			   (position-p (cons i pos) (cons fn args)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.5 Disabling the theory
-;;; 
+;;; ············································································
 
 (defconst *tree-structure-of-terms*
   '(position-p-append occurrence-append replace-term-append
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/unification-pattern.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/unification-pattern.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/unification-pattern.lisp
@@ -216,12 +216,12 @@
 
 
 ;;; Equivalence for each rule (some rules do not need auxiliary lemmas)
-;;; 
+;;; ···································································
 
 
-;;; 
+;;; ····················
 ;;; 2.1.1 rule DECOMPOSE
-;;; 
+;;; ····················
 (local
  (defun induction-transform-sel-decompose-rule (l1 l2)
    (if (or (atom l1) (atom l2))
@@ -241,9 +241,9 @@
 
 
 
-;;; 
+;;; ·····················
 ;;; 2.1.2  rule ELIMINATE
-;;; 
+;;; ·····················
 
 ;;; If sigma is a solution of sol, and x is a variable, then
 ;;; sigma(sol(x)) = sol(x).
@@ -258,7 +258,7 @@
 	       (apply-subst flg sigma (val x sol))
 	       (val x sigma)))))
 
-;;; If sigma is a solution of S, sigma = sigma  S
+;;; If sigma is a solution of S, sigma = sigma · S
 
   (defthm substitutions-solution-system
     (implies (solution sigma S)
@@ -287,9 +287,9 @@
 	     (solution sigma s)))))
 
 
-;;; 
+;;; ················
 ;;; 2.1.3 rule CHECK
-;;; 
+;;; ················
 
 ;;; GOAL:
 ;;; Prove that x = term, when x is not in term and is not term, has no
@@ -377,9 +377,9 @@
 	    :use ((:instance
 		   transform-sel-check-rule-not-equal-size))))))
 
-;;; 
+;;; ···················
 ;;; 2.1.4 rule CONFLICT
-;;; 
+;;; ···················
 
 ;;; The equation (f t1 ... tn) = (g s1 ... sm), with f/=g has no
 ;;; solution:
@@ -392,9 +392,9 @@
 	    (not (equal (apply-subst t sigma t1)
 			(apply-subst t sigma t2))))))
 
-;;; 
+;;; ····················
 ;;; 2.1.5 rule NOT-PAIR
-;;; 
+;;; ····················
 
 ;;; If sigma(t1...tn . a) = sigma(s1...sm . b), then n=m and a=b:
 ;;; ======= Corolary: The equation (f t1 ... tn . a) = (g s1 ... sm . b)
@@ -417,9 +417,9 @@
 			 (apply-subst t sigma t2)))))))
 
 
-;;; 
+;;; ··················
 ;;; 2.1.6 And finally:
-;;; 
+;;; ··················
 
 ;;; Three lemmas to state that transform-mm-sel preserves the set of
 ;;; solutions:
@@ -498,9 +498,9 @@
 ;;; ELIMINATE needs help form the user
 
 
-;;; 
+;;; ····················
 ;;; 2.2.1 rule DECOMPOSE
-;;; 
+;;; ····················
 
 ;;; Properties to prove that, for the rule decompose, the variables of
 ;;; the system S are disjoint from the domain of sol.
@@ -529,9 +529,9 @@
 				(variables nil l2)))))))
 
 
-;;; 
+;;; ····················
 ;;; 2.2.2 rule ELIMINATE
-;;; 
+;;; ····················
 
 ;;; Properties to prove that, for the rule eliminate, the variables of
 ;;; the system S and the co-domain of sol are disjoint from the domain
@@ -634,9 +634,9 @@
 		   (a (system-var (apply-syst sigma S)))))))))
 
 
-;;; 
+;;; ····················
 ;;; 2.2.3 And finally
-;;; 
+;;; ····················
 
 (local
  (defthm transform-mm-sel-preserves-idempotency
@@ -662,9 +662,9 @@
 
 ;;; This section is needed for guard verification.
 
-;;; 
+;;; ············································································
 ;;; 2.3.1 preservation of the system-p property
-;;; 
+;;; ············································································
 
 (local
  (encapsulate
@@ -723,9 +723,9 @@
     :hints (("Goal" :in-theory (disable substitution-s-p))))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.3.2 preservation of the system-p property
-;;; 
+;;; ············································································
 
 (local
  (encapsulate
@@ -814,16 +814,16 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 2.4.1 transform-mm-sel does not add new variables
-;;; 
+;;; ············································································
 
 ;;; Goal:
 ;;; We will prove that the variables of S are a subset of
 ;;; the variables of the transformed, for every rule.
 
 ;;; Some lemmas about eliminate
-;;; 
+;;; ···························
 
 (local
   (defthm subsetp-variables-delete
@@ -855,7 +855,7 @@
  			    (S (eliminate ecu S))))))))
 
 ;;; Lemmas dealing with length, setps and subsetps
-;;; 
+;;; ··············································
 
 (local
  (defthm len-subsetp-setp
@@ -874,7 +874,7 @@
   ()
 
 ;;; Main lemma (in terms of subsetp)
-;;; 
+;;; ································
 
   (local
    (defthm transform-sel-does-not-add-new-variables
@@ -890,7 +890,7 @@
 			       (S (car S-sol)))))))
 
 ;;; The main lemma (the previous lemma in terms of n-system-var)
-;;; 
+;;; ····························································
 
   (defthm
     transform-does-not-increases-n-variables
@@ -902,9 +902,9 @@
 	     (disable system-var transform-mm-sel))))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.4.2 The rule eliminate eliminates one variable from S
-;;; 
+;;; ············································································
 
 ;;; This subsection is needed to show that when n-system-var does not
 ;;; change after one step of transformation, then the rule ELIMNATE has
@@ -978,9 +978,9 @@
 ;;; complicated.
 
 
-;;; 
+;;; ············································································
 ;;; 2.4.3 How we deal with selection (second part).
-;;; 
+;;; ············································································
 
 ;;; equal-set is not a congruence w.r.t. size-system and
 ;;; n-variables-right-hand-side. See observaciones.txt to understand why
@@ -1069,9 +1069,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 2.4.4 Size-system does not increase (when n-variables remains the same)
-;;; 
+;;; ············································································
 
 ;;; Technical lemma:
 
@@ -1109,10 +1109,10 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 2.4.5 n-variables-right-hand-side does not increase (when the two above
 ;;; quantities remain the same)
-;;; 
+;;; ············································································
 
 ;;; Lemmas:
 
@@ -1198,9 +1198,9 @@
 
 (local (in-theory (disable n-variables-rhs-cons-select-and-delete-one)))
 
-;;; 
+;;; ············································································
 ;;; 2.4.6 Compiling the previous results: the  main termination property
-;;; 
+;;; ············································································
 
 ;;; We disable some definition and lemmas
 
@@ -1218,7 +1218,7 @@
 
 
 ;;; AND THE MAIN TERMINATION THEOREMS
-;;; 
+;;; ·································
 
 (defthm ordinalp-unification-measure
   (e0-ordinalp (unification-measure S-sol)))
@@ -1267,9 +1267,9 @@
 ;;; ----------------------------------------------------------------------------
 
 
-;;; 
+;;; ··········································
 ;;; 3.2.1 solve-system-sel preserves solutions
-;;; 
+;;; ··········································
 
 ;;; A technical lemma
 
@@ -1313,9 +1313,9 @@
 (local (in-theory (enable union-systems)))
 
 
-;;; 
+;;; ·············································
 ;;; 3.2.2 solve-system-sel preserves idempotence
-;;; 
+;;; ·············································
 
 
 (local (in-theory (disable disjointp-conmutative)))
@@ -1336,9 +1336,9 @@
    :hints (("Goal" :induct (solve-system-sel S-sol)))))
 
 
-;;; 
+;;; ····························································
 ;;; 3.2.3 solve-system-sel preserves system-p and substitution-p
-;;; 
+;;; ····························································
 
 ;;; Closure property
 
@@ -1380,9 +1380,9 @@
 ;;; 4.2 Main properties of mgs-sel
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ······························································
 ;;; THEOREM 4.2.1. If S is solvable, then (mgs-sel S) succeeds.
-;;; 
+;;; ······························································
 
 (defthm mgs-sel-completeness
   (implies (solution sigma S)
@@ -1400,10 +1400,10 @@
    (solution sigma (first (solve-system-sel S-sol)))))
 
 
-;;; 
+;;; ·······································································
 ;;; THEOREM 4.2.2: If (mgs-sel S) succeeds, then the system is solvable
 ;;; (and a solution is (first (mgs-sel S))
-;;; 
+;;; ·······································································
 
 (local
  (defthm mgs-sel-soundness
@@ -1415,9 +1415,9 @@
 		       (S-sol (cons S nil))
 		       (sigma (first (mgs-sel S)))))))))
 
-;;; 
+;;; ····················································
 ;;; THEOREM 4.2.3: (first (mgs-sel S)) is idempotent.
-;;; 
+;;; ·····················································
 
 
 (local
@@ -1428,10 +1428,10 @@
 ;;; REMARK: This is true even if (mgs-sel S) fails
 
 
-;;; 
+;;; ···························································
 ;;; THEOREM 4.2.4:  The substitution returned by mgs-sel is
 ;;; substitution-p, whenever its input system is system-p
-;;; 
+;;; ····························································
 
 ;;; This theorem is needed for guard verification.
 
@@ -1449,10 +1449,10 @@
 
 
 
-;;; 
+;;; ··································································
 ;;; THEOREM 4.2.5: If sigma is a solution of S, (first (mgs-sel S))
 ;;; subsumes sigma.  (thus, (first (mgs-sel S)) is a mgs of S)
-;;; 
+;;; ···································································
 
 ;;; Lemma: If sigma is a solution of S, then for all term, (first
 ;;; (mgs-sel S))(term) subsumes sigma(term), with the matching
@@ -1524,9 +1524,9 @@
 ;;; t1 t2)))
 
 
-;;; 
+;;; ······································································
 ;;; THEOREM 5.2.1: If t1 and t2 are unifiable, then (unifiable-sel t1 t2).
-;;; 
+;;; ······································································
 
 (defthm  unifiable-sel-completeness
   (implies (equal (instance t1 sigma)
@@ -1538,10 +1538,10 @@
 		       (S (list (cons t1 t2)))))))
 
 
-;;; 
+;;; ········································································
 ;;; THEOREM 5.2.2: If (unifiable-sel t1 t2), t1 and t2 are unifiable
 ;;; (and (mgu-sel t1 t2) is an unifier).
-;;; 
+;;; ········································································
 
 
 (defthm unifiable-sel-soundness
@@ -1553,17 +1553,17 @@
 		       (S (list (cons t1 t2))))))))
 
 
-;;; 
+;;; ········································································
 ;;; THEOREM 5.2.3: (mgu-sel t1 t2) is idempotent.
-;;; 
+;;; ········································································
 
 (defthm mgu-sel-idempotent
   (idempotent (mgu-sel t1 t2)))
 
-;;; 
+;;; ········································································
 ;;; THEOREM 5.2.4: If t1 and t2 are terms of a given signature, then mgu-sel
 ;;; returns a substitution of that signature
-;;; 
+;;; ········································································
 
 
 
@@ -1573,10 +1573,10 @@
 
 
 
-;;; 
+;;; ········································································
 ;;; THEOREM 5.2.5: If sigma is an unifier of t1 and t2, then (mgu-sel t1 t2)
 ;;; subsumes sigma (thus, (mgu-sel t1 t2) is a mgu of t1 and t2).
-;;; 
+;;; ········································································
 
 (defthm mgu-sel-most-general-unifier
   (implies (equal (instance t1 sigma)
Index: acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/unification.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/unification.lisp
+++ acl2-8.4dfsg/books/workshops/2002/ruiz-alonso-hidalgo-martin-theory-terms/support/unification.lisp
@@ -43,10 +43,10 @@
 ;;; 1.1 A particular version of transform-mm-sel
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ············································································
 ;;; 1.1.1 A particular "selection" function. If we detect an inmediate fail,
 ;;; we select it.
-;;; 
+;;; ············································································
 
 (defun sel-unif (S)
   (declare (xargs :guard (and (consp S) (system-p S))))
@@ -69,9 +69,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 1.1.2 Some lemmas needed for guard verification:
-;;; 
+;;; ············································································
 
 (encapsulate
  ()
@@ -108,9 +108,9 @@
 		 (variable-p (car (sel-unif S))))
 	    (eqlablep (car (sel-unif S)))))
 
-;;; 
+;;; ············································································
 ;;; 1.1.3 The function transform-mm
-;;; 
+;;; ············································································
 
 
  (defun transform-mm (S sol)
@@ -354,7 +354,7 @@
 ;;; Most of these properties are obtained by functional instantiation.
 
 ;;; Completeness
-;;; 
+;;; ············
 
 (defthm  mgu-completeness
   (implies (equal (instance t1 sigma)
@@ -376,7 +376,7 @@
 ;;; The hint is not necessary, but makes the proof shorter.
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 
 (defthm mgu-soundness
@@ -397,7 +397,7 @@
 
 
 ;;; Idempotence
-;;; 
+;;; ···········
 
 (defthm mgu-idempotent
   (idempotent (mgu t1 t2))
@@ -416,7 +416,7 @@
 
 
 ;;; Generality of the unifier
-;;; 
+;;; ·························
 
 (defthm mgu-most-general-unifier
   (implies (equal (instance t1 sigma)
@@ -437,7 +437,7 @@
 
 
 ;;; Substitution-s-p (closure property of mgu)
-;;; 
+;;; ··············································
 
 
 (defthm mgu-substitution-s-p
@@ -458,7 +458,7 @@
 
 
 ;;; Substitution-p (needed for guard verification)
-;;; 
+;;; ··············································
 
 
 (defthm mgu-substitution-p
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/basic.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/basic.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/basic.lisp
@@ -753,7 +753,7 @@
 ;;;
 ;;;============================================================================
 
-;; Ya incluido en la versin 2-8
+;; Ya incluido en la versión 2-8
 ;; (defun natp (n)
 ;;   (declare (xargs :guard t))
 ;;   (and (integerp n)
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/dag-unification-rules.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/dag-unification-rules.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/dag-unification-rules.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; dag-unification-rules.lisp
-;;; Ttulo: Unification rules on term dags
+;;; Título: Unification rules on term dags
 ;;; ============================================================================
 
 #| To certify this book:
@@ -22,7 +22,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
@@ -211,12 +211,12 @@
 ;;; variables. We define the "bounded" version and the "relaxed"
 ;;; version.
 
-;;; NOTA: La guarda de esta funcin sera muy rara, ya que dag-p
+;;; NOTA: La guarda de esta función sería muy rara, ya que dag-p
 ;;; necesita term-graph-p, que es como bounded-term-graph-p pero para
-;;; n=(len g). As que ha optado por no ponerle guarda( creo que esta no
+;;; n=(len g). Así que ha optado por no ponerle guarda( creo que esta no
 ;;; tinene ni que ejecutarse ni que usarse en una guarda) y luego
 ;;; definir well-formed-term-dag-p igual que esto pero con n=(len g) y
-;;; esa si ponerle guarda. Adems, pongo una regla de reescritura que
+;;; esa si ponerle guarda. Además, pongo una regla de reescritura que
 ;;; relacione ambas cosas.
 (defun bounded-well-formed-term-dag-p (g n)
   (and (bounded-term-graph-p g n)
@@ -281,7 +281,7 @@
 ;;; system and the substitution.
 
 
-;;; NOTA: aqu se aplica el mismo comentario que antes
+;;; NOTA: aquí se aplica el mismo comentario que antes
 (defun bounded-well-formed-upl (upl n)
   (and (bounded-nat-pairs-true-listp (first upl) n)
        (bounded-nat-substitution-p (second upl) n)
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/dags.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/dags.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/dags.lisp
@@ -1,6 +1,6 @@
 ;;;============================================================================
 ;;; dags.lisp
-;;; Ttulo: Term dags in ACL2
+;;; Título: Term dags in ACL2
 ;;;============================================================================
 
 #| To certify this book:
@@ -20,7 +20,7 @@
 
 ;;;============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;;============================================================================
 
@@ -589,7 +589,7 @@
 	(not (dag-p-aux hs rp g)))))
 
 ;;; Finally, the soundness theorem:
-;;; 
+;;; ·······························
 
 (defthm dag-p-soundness
   (implies (not (dag-p g))
@@ -633,7 +633,7 @@
 
 
 ;;; The main lemma for completeness:
-;;; 
+;;; ································
 
 (local
  (defthm dag-p-aux-completeness-main-lemma
@@ -1680,7 +1680,7 @@
 
 
 ;;; RECALL: These two theorems would allow us to define functions like these:
-;;; 
+;;; ·········································································
 
 
 ; (defun occur-check-l (flg x h g)
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/matching.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/matching.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/matching.lisp
@@ -89,9 +89,9 @@
 ;;; ----------------------------------------------------------------------------
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.1 How we deal with selection.
-;;; 
+;;; ············································································
 
 
 ;;; Firs we prove that equal-set is a congruence w.r.t. the second
@@ -139,9 +139,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.2 transform-subs-sel preserves the set of matchers.
-;;; 
+;;; ············································································
 
 
 (local
@@ -211,7 +211,7 @@
 	      (not (matcher sigma S)))))
 
 ;;; The three main theorems of this subsubsection
-;;; 
+;;; ·············································
 
   (defthm transform-subs-sel-preserves-matchers-1
     (implies
@@ -235,10 +235,10 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.3 (system-substitution (cdr S-match)) is an invariant in the rules
 ;;;     of transformation.
-;;; 
+;;; ············································································
 
 
 
@@ -261,9 +261,9 @@
      (system-substitution (cdr (transform-subs-sel S-match)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 1.2.4 Main property of the property system-substitution
-;;; 
+;;; ············································································
 
 
 (local
@@ -362,7 +362,7 @@
 			(length-term nil args2))))))
 
 ;;; And the main result:
-;;; 
+;;; ····················
 
   (defthm transform-subs-sel-decreases-length-of-first-system
     (implies (not (normal-form-syst S-match))
@@ -460,7 +460,7 @@
 
 ;;; Three lemmas to state that the set of matchers is preserved by
 ;;; subs-system-sel
-;;; 
+;;; ··········································································
 
 (local
  (defthm subs-system-sel-preserves-matchers-1
@@ -488,7 +488,7 @@
 (in-theory (enable union-systems))
 
 ;;; subs-system-sel preserves the property of being a system-substitution.
-;;; 
+;;; ··································································
 
 (local
  (defthm subs-system-sel-preserves-system-substitution
@@ -496,7 +496,7 @@
 	   (system-substitution (cdr (subs-system-sel S-match))))))
 
 ;;; Guard verification: a substitution-s-p is returned
-;;; 
+;;; ···················································
 
 (local
  (defthm
@@ -604,7 +604,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 
 (defthm subs-sel-soundness
@@ -618,7 +618,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ············
 
 
 (defthm subs-sel-completeness
@@ -632,7 +632,7 @@
 
 ;;; Closure property:
 ;;; (the following theorem is needed for guard verification)
-;;; 
+;;; ························································
 
 
 (defthm matching-sel-substitution-s-p
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/prefix-unification-rules.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/prefix-unification-rules.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/prefix-unification-rules.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; prefix-unification-rules.lisp
-;;; Ttulo: Unification as transformation rules (using a prefix representation of terms)
+;;; Título: Unification as transformation rules (using a prefix representation of terms)
 ;;; ============================================================================
 
 
@@ -20,7 +20,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/q-dag-unification-rules.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/q-dag-unification-rules.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/q-dag-unification-rules.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; q-dag-unification-rules.lisp
-;;; Ttulo: Unification rules on term dags for the quadratic algorithm
+;;; Título: Unification rules on term dags for the quadratic algorithm
 ;;; 12-03-03
 ;;; ============================================================================
 
@@ -21,7 +21,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/q-dag-unification-st.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/q-dag-unification-st.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/q-dag-unification-st.lisp
@@ -1,6 +1,6 @@
 ;;;============================================================================
 ;;; q-dag-unification-st.lisp
-;;; Ttulo: A quadratic unification algorithm using stobjs
+;;; Título: A quadratic unification algorithm using stobjs
 ;;;============================================================================
 
 #| To be certified:
@@ -15,7 +15,7 @@
 
 ;;;============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;;============================================================================
 
@@ -743,7 +743,7 @@
 
 ;;; Este disable es importante, puesto que todas las reglas anteriores
 ;;; (y las que siguen)
-;;; llevan nth en su lado izquierdo. Por tanto, slo habilitaremos nth
+;;; llevan nth en su lado izquierdo. Por tanto, sólo habilitaremos nth
 ;;; en caso de que sea estrictamente necesario.
 (local (in-theory (disable nth)))
 
@@ -1129,7 +1129,7 @@
 (in-theory (disable tbs-as-system-st solved-as-system-st))
 
 
-;; Este funcin es solo para evitarme escribir:
+;; Este función es solo para evitarme escribir:
 
 (local
  (defun well-formed-dag-system-st-bis (S td)
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/q-dag-unification.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/q-dag-unification.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/q-dag-unification.lisp
@@ -1,6 +1,6 @@
 ;; ============================================================================
 ;;; q-dag-unification.lisp
-;;; Ttulo: A quadratic dag based unification algorithm
+;;; Título: A quadratic dag based unification algorithm
 ;;; ============================================================================
 
 #| To certify this book:
@@ -20,7 +20,7 @@
 
 ;;;============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;;============================================================================
 
@@ -356,7 +356,7 @@
 		      (term-dag-non-variable-p (cdr (first requations))
 					       g)
 		      (not (term-dag-is-p (car (first requations)) g))
-;;; la anterior condicin es redundante, pero necesaria para la guarda
+;;; la anterior condición es redundante, pero necesaria para la guarda
 		      (term-dag-variable-p (car (first requations)) g)
 		      (equation-justify-equality
 		       (car rargs1) (car rargs2)
@@ -419,8 +419,8 @@
 	 (idc (first id-equ)))
     (and
      (equal idc 'id)
-     (let* ((id1 (second id-equ)) ;;; Este let* est aqu por la
-				  ;;; verificacin de guardas
+     (let* ((id1 (second id-equ)) ;;; Este let* está aquí por la
+				  ;;; verificación de guardas
 	    (id2 (third id-equ))
 	    (p1 (dagi-l id1 g))
 	    (p2 (dagi-l id2 g)))
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/subsumption-subst.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/subsumption-subst.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/subsumption-subst.lisp
@@ -26,15 +26,15 @@
 ;;; Our goal is to define the subsumption relation between
 ;;; substitutions. In the literature, this relation is defined in this
 ;;; way:
-;;;     sigma <= delta iff (exists gamma) gammasigma = delta
-;;; where "" stands for composition.
+;;;     sigma <= delta iff (exists gamma) gamma·sigma = delta
+;;; where "·" stands for composition.
 
 ;;; Note that equality between substitutions is functional equality (we cannot
 ;;; use equal), so we reformulate this property as:
 
 ;;; (*) sigma <= delta iff (exists gamma)
 ;;;                        s.t. for all term
-;;;                        gammasigma(term) = delta(term)
+;;;                        gamma·sigma(term) = delta(term)
 
 
 ;;; Our goal in this book is to define the subsumption relation between
@@ -285,9 +285,9 @@
 ;;; if (subs-sust sigma delta)
 ;;; WE DISTINGUISH THREE CASES.
 
-;;; 
+;;; ············································································
 ;;; 3.1.1 Case 1: x is a variable outside V
-;;; 
+;;; ············································································
 
 
 
@@ -303,14 +303,14 @@
    :hints (("Goal" :in-theory (enable x-not-in-domain-remains-the-same)))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.1.2. Case 2: x is a variable of (domain-var sigma)
-;;; 
+;;; ············································································
 
 
 ;;; 3.1.2.1 A lemma for this case 2:
 ;;; subs-subst composed with sigma is equal to delta in V.
-;;; 
+;;; ······················································
 
 (local
  (encapsulate
@@ -373,7 +373,7 @@
 (local (in-theory (disable subs-subst matching-subst)))
 
 ;;; 3.1.2.2 Another lemma for case 2:
-;;; 
+;;; ·······························
 
 (local
  (defthm variables-co-domain-var
@@ -383,7 +383,7 @@
 
 
 ;;; 3.1.2.3 The main result for Case 2
-;;; 
+;;; ································
 
 (local
  (defthm
@@ -396,14 +396,14 @@
 		   (val x delta)))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.1.3. Case 3: x in V but not in (domain-var sigma)
-;;; 
+;;; ············································································
 
 
 ;;; 3.1.3.1 A lemma for Case 3
 ;;; In this case, matching and matching-subst-r take the same values.
-;;; 
+;;; ·································································
 
 (local
  (defthm
@@ -472,7 +472,7 @@
 
 
 ;;; With terms and list of terms (not only with variables)
-;;; 
+;;; ······················································
 
 (local
  (defthm
@@ -512,7 +512,7 @@
 ;;; following version will be used as a rewrite rule.
 
 ;;; With terms but without using composition
-;;; 
+;;; ········································
 
 (defthm
   subs-subst-implies-matching-subst-r-appplied-to-sigma-term-is-delta-term
@@ -526,7 +526,7 @@
 
 
 ;;; With respect to subsumption between terms
-;;; 
+;;; ·········································
 
 
 ;;; Trivial consequence of completeness of subsumption and the previous
@@ -563,7 +563,7 @@
 ;;; existence of two substitutions, called sigma-w and delta-w and the
 ;;; only property we will assume about them is that sigma-w <=
 ;;; delta-w. That is, exists another substitution gamma-w such that
-;;; delta-w = gamma-wsigma-w.
+;;; delta-w = gamma-w·sigma-w.
 
 ;;; We will use encapsulate for that purpose. Let sigma-w, delta-w and
 ;;; gamma-w three susbtitutions such that delta-w is functionally equal
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/subsumption.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/subsumption.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/subsumption.lisp
@@ -1,7 +1,7 @@
 ;;; subsumption.lisp Definition of a particular RULE-BASED matching
 ;;; algorithm between terms.  We use functional instantion of the
 ;;; pattern given in matching.lisp Using this algorithm, we define the
-;;; subsumption relation between terms and lists of terms in a
+;;; subsumption relńation between terms and lists of terms in a
 ;;; constructive way, and we prove that subsumption is a preorder.
 ;;; Created: 11-10-99 Last revison: 07-12-2000
 ;;; =============================================================================
@@ -287,7 +287,7 @@
 ;;; Most of these properties are obtained by functional instantiation.
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 (defthm subs-soundness
   (implies (subs t1 t2)
@@ -298,7 +298,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ·············
 
 (defthm subs-completeness
   (implies (equal (instance t1 sigma) t2)
@@ -308,7 +308,7 @@
 	   (:instance match-mv-completeness (S (list (cons t1 t2)))))))
 
 ;;; Substitution-s-p (closure property)
-;;; 
+;;; ···································
 
 
 (defthm matching-substitution-s-p
@@ -318,7 +318,7 @@
 	   (:instance match-mv-substitution-s-p (S (list (cons t1 t2)))))))
 
 ;;; Substitution-p (needed for guard verification)
-;;; 
+;;; ··············································
 
 
 (defthm matching-substitution-p
@@ -409,7 +409,7 @@
    (second (pair-args l1 (apply-subst nil sigma l1)))))
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 
 (defthm subs-list-soundness
@@ -421,7 +421,7 @@
 
 
 ;;; Completeness
-;;; 
+;;; ·············
 
 (defthm subs-list-completeness
   (implies (equal (apply-subst nil sigma l1) l2)
@@ -431,7 +431,7 @@
 	   (:instance match-mv-completeness (S (first (pair-args l1 l2)))))))
 
 ;;; Substitution-s-p (closure property)
-;;; 
+;;; ···································
 
 
 (defthm matching-list-substitution-s-p
@@ -444,7 +444,7 @@
 
 
 ;;; Substitution-p (needed for guard verification)
-;;; 
+;;; ··············································
 
 
 (defthm matching-list-substitution-p
@@ -498,7 +498,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;;; Subsumption reflexive
-;;;; 
+;;;; ·····················
 
 (defthm subsumption-reflexive
    (subs t1 t1)
@@ -508,7 +508,7 @@
 
 
 ;;;; Subsumption transitive
-;;;; 
+;;;; ······················
 
 
 (defthm subsumption-transitive
@@ -528,7 +528,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;; An useful rule:
-;;; 
+;;; ···············
 
 (defthm subsumption-apply-subst
   (subs term (instance term sigma))
@@ -536,7 +536,7 @@
 				  (t1 term) (t2 (instance term sigma))))))
 
 ;;; Variables are minimum elements in this quasi-order
-;;; 
+;;; ··················································
 
 (defthm variable-minimum-subsumption
   (implies (variable-p x)
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/terms-as-dag.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/terms-as-dag.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/terms-as-dag.lisp
@@ -1,6 +1,6 @@
 ;;; ============================================================================
 ;;; terms-as-dag.lisp
-;;; Ttulo: Storing first--order terms as dags
+;;; Título: Storing first--order terms as dags
 ;;; ============================================================================
 
 #| To certify this book:
@@ -20,7 +20,7 @@
 
 ;;; ============================================================================
 ;;;
-;;; 0) Introduccin
+;;; 0) Introducción
 ;;;
 ;;; ============================================================================
 
Index: acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/terms.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2004/ruiz-et-al/support/terms.lisp
+++ acl2-8.4dfsg/books/workshops/2004/ruiz-et-al/support/terms.lisp
@@ -939,7 +939,7 @@
        (disjointp (variables nil (co-domain S)) (domain S))))
 
 ;;; REMARK: In the literature, idempotent substitutions are defined as
-;;; substitutions sigma such that sigmasigma = sigma. But this
+;;; substitutions sigma such that sigma·sigma = sigma. But this
 ;;; definition involves functional equality. We will see that the above
 ;;; definition implies this property (see main-property-mgs in the book
 ;;; unification-definition.lisp) Nevertheless, the definition does not
@@ -949,9 +949,9 @@
 ;;; functionally equivalent idempotent (in our sense) substitution, ((x
 ;;; . y)) in this case.
 
-;;; 
+;;; ············································································
 ;;; 3.3.1 The main property of idempotent substitutions.
-;;; 
+;;; ············································································
 
 ;;; .... PROOF PLAN:
 
@@ -1103,9 +1103,9 @@
 ;;; 4.2 Some results concerning the tree structure of a term
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ············································································
 ;;; 4.2.1 Concatenation of positions
-;;; 
+;;; ············································································
 
 (defthm position-p-append
   (implies (position-p p1 term)
@@ -1128,9 +1128,9 @@
 					      q x)))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.2 Substitutions and positions
-;;; 
+;;; ············································································
 
 (defthm nth-apply-subst
   (implies (and (integerp i)
@@ -1165,9 +1165,9 @@
 	    (instance (replace-term term pos t1) sigma))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.3 Prefix positions
-;;; 
+;;; ············································································
 
 (local
  (defthm equal-len-replace-list
@@ -1202,9 +1202,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.4 Disjoint positions
-;;; 
+;;; ············································································
 
 (local
  (defun induct-position-p-disjoint (pos1 pos2 term)
@@ -1267,9 +1267,9 @@
 			   (position-p (cons i pos) (cons fn args)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 4.2.5 Disabling the theory
-;;; 
+;;; ············································································
 
 (defconst *tree-structure-of-terms*
   '(position-p-append occurrence-append replace-term-append
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/coe-fld.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/coe-fld.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/coe-fld.lisp
@@ -42,22 +42,22 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
 ;;; Anillo abeliano de coeficientes. El conjunto de los coeficientes
 ;;; se representa como un anillo abeliano abstracto mediante un
-;;; encapsulado. El conjunto de los nmeros de ACL2 con su
-;;; interpretacin habitual sirve como modelo de la teora generada.
+;;; encapsulado. El conjunto de los números de ACL2 con su
+;;; interpretación habitual sirve como modelo de la teoría generada.
 ;;;
 ;;; Notas generales:
 ;;;
-;;; Puede ser interesante comparar esta formalizacin con la que
-;;; aparece en los libros sobre aritmtica de Kaufmann, Brock y
+;;; Puede ser interesante comparar esta formalización con la que
+;;; aparece en los libros sobre aritmética de Kaufmann, Brock y
 ;;; Cowles.
 ;;;
 ;;; Se han incluido algunos teoremas que se deducen inmediatamente de
-;;; otros por aplicacin directa de la conmutatividad. Estos teoremas
-;;; son innecesarios desde un punto de vista lgico, pero evitan el
+;;; otros por aplicación directa de la conmutatividad. Estos teoremas
+;;; son innecesarios desde un punto de vista lógico, pero evitan el
 ;;; abuso de la conmutatividad.
 ;;; ------------------------------------------------------------------
 #|
@@ -140,21 +140,21 @@ To certify this book, first, create a wo
 	  fdp (a)
 	  (acl2-numberp a)))
 
-  ;;; Primera operacin
+  ;;; Primera operación
 
  (local
   (defun + (a b)
 ;   (declare (xargs :guard (and (coeficientep a) (coeficientep b))))
     (ACL2::+ a b)))
 
-  ;;; Segunda operacin
+  ;;; Segunda operación
 
  (local
   (defun * (a b)
 ;   (declare (xargs :guard (and (coeficientep a) (coeficientep b))))
     (ACL2::* a b)))
 
-  ;;; Inverso de la primera operacin
+  ;;; Inverso de la primera operación
 
  (local
   (defun - (a)
@@ -166,7 +166,7 @@ To certify this book, first, create a wo
 ;   (declare (xargs :guard (coeficientep a)))
     (ACL2::/ a)))
 
-  ;;; Neutro de la primera operacin
+  ;;; Neutro de la primera operación
 
 ;;   (local
 ;;     (defun nulo ()
@@ -175,7 +175,7 @@ To certify this book, first, create a wo
  (local (defun 0_f ()
 	  0))
 
-  ;;; Neutro de la segunda operacin
+  ;;; Neutro de la segunda operación
 
 ;;   (local
 ;;     (defun identidad ()
@@ -184,7 +184,7 @@ To certify this book, first, create a wo
  (local (defun 1_f ()
 	  1))
 
-  ;;; Igualdad sintctica
+  ;;; Igualdad sintáctica
 
 ;;   (defmacro = (a b)
 ;;     `(equal ,a ,b))
@@ -200,7 +200,7 @@ To certify this book, first, create a wo
   ;;; -------
   ;;; Field Axioms:
 
- ;;; El reconocedor es una funcin booleana
+ ;;; El reconocedor es una función booleana
 
 ;;   (defthm booleanp-coeficientep
 ;;     (booleanp (coeficientep a))
@@ -463,7 +463,7 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :use Congruence-Laws)))
 
-  ;;; Conmutatividad de la primera operacin
+  ;;; Conmutatividad de la primera operación
 
 ;;   (defthm |a + b = b + a|
 ;;     (implies (and (coeficientep a) (coeficientep b))
@@ -476,7 +476,7 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :use Commutativity-Laws)))
 
-  ;;; Asociatividad de la primera operacin
+  ;;; Asociatividad de la primera operación
 
 ;;   (defthm |(a + b) + c = a + (b + c)|
 ;;     (implies (and (coeficientep a) (coeficientep b) (coeficientep c))
@@ -490,7 +490,7 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :use Associativity-Laws)))
 
-  ;;; Neutro de la primera operacin
+  ;;; Neutro de la primera operación
 
 ;;   (defthm |0 + a = a|
 ;;     (implies (coeficientep a)
@@ -502,7 +502,7 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :use Left-Unicity-Laws)))
 
-  ;;; Conmutatividad de la segunda operacin
+  ;;; Conmutatividad de la segunda operación
 
 ;;   (defthm |a * b = b * a|
 ;;     (implies (and (coeficientep a) (coeficientep b))
@@ -515,7 +515,7 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :use Commutativity-Laws)))
 
-  ;;; Asociatividad de la segunda operacin
+  ;;; Asociatividad de la segunda operación
 
 ;;   (defthm |(a * b) * c = a * (b * c)|
 ;;      (implies (and (coeficientep a) (coeficientep b) (coeficientep c))
@@ -529,7 +529,7 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :use Associativity-Laws)))
 
-  ;;; Neutro de la segunda operacin
+  ;;; Neutro de la segunda operación
 
 ;;   (defthm |1 * a = a|
 ;;     (implies (coeficientep a)
@@ -541,7 +541,7 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :use Left-Unicity-Laws)))
 
-  ;;; Inverso de la primera operacin
+  ;;; Inverso de la primera operación
 
 ;;   (defthm |a + (- a) = 0|
 ;;     (implies (coeficientep a)
@@ -560,7 +560,7 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :use Right-Inverse-Laws)))
 
-  ;;; Distributividad de la segunda operacin respecto a la primera
+  ;;; Distributividad de la segunda operación respecto a la primera
 
 ;;   (defthm |a * (b + c) = (a * b) + (a * c)|
 ;;     (implies (and (coeficientep a) (coeficientep b) (coeficientep c))
@@ -575,7 +575,7 @@ To certify this book, first, create a wo
 	   :use Left-Distributivity-Law)))
 
 ;;; -----------------------------------------------------------------------
-;;; El inverso debe ser invisible para la primera operacin y para s mismo
+;;; El inverso debe ser invisible para la primera operación y para sí mismo
 ;;; -----------------------------------------------------------------------
 
 ;; (ACL2::set-invisible-fns-table ((+ -) (- -)))
@@ -642,7 +642,7 @@ To certify this book, first, create a wo
 		(fdp (double-rewrite c)))
 	   (= (* (+ a b) c) (+ (* a c) (* b c)))))
 
-;;; Teorema de cancelacin
+;;; Teorema de cancelación
 
 ;; (defthm |a + c = b + c <=> a = b|
 ;;   (implies (and (coeficientep a) (coeficientep b) (coeficientep c))
@@ -666,8 +666,8 @@ To certify this book, first, create a wo
 
 ;;; NOTA:
 ;;;
-;;; Estos teoremas son innecesarios desde un punto de vista lgico
-;;; pero son tiles en las subsecuentes demostraciones.
+;;; Estos teoremas son innecesarios desde un punto de vista lógico
+;;; pero son útiles en las subsecuentes demostraciones.
 
 ;; (local
 ;;   (defthm |a + b = b <=> a = 0|
@@ -701,16 +701,16 @@ To certify this book, first, create a wo
 	     :in-theory (disable |a + c = b + c <=> a = b|)
 	     :use (:instance |a + c = b + c <=> a = b| (a b) (b (- a)) (c a))))))
 
-;;; Complemento a la conmutatividad y la asociatividad de la primera operacin
+;;; Complemento a la conmutatividad y la asociatividad de la primera operación
 
 ;;; NOTA:
 ;;;
-;;; Dada una operacin, las reglas generadas por este teorema y los
+;;; Dada una operación, las reglas generadas por este teorema y los
 ;;; axiomas de conmutatividad y asociatividad permiten decidir una
-;;; igualdad de dos trminos en los que slo intervienen smbolos sin
-;;; interpretacin y dicha operacin. Esto se debe a que ACL2 emplea
-;;; un sistema de reescritura ordenada. Vase Ordered Rewriting and
-;;; Confluence, por Martin y Nipkow.
+;;; igualdad de dos términos en los que sólo intervienen símbolos sin
+;;; interpretación y dicha operación. Esto se debe a que ACL2 emplea
+;;; un sistema de reescritura ordenada. Véase «Ordered Rewriting and
+;;; Confluence», por Martin y Nipkow.
 
 ;; (defthm |a + (b + c) = b + (a + c)|
 ;;   (implies (and (coeficientep a) (coeficientep b) (coeficientep c))
@@ -730,11 +730,11 @@ To certify this book, first, create a wo
 	   :use (|(a + b) + c = a + (b + c)|
 		 (:instance |(a + b) + c = a + (b + c)| (a b) (b a))))))
 
-;;; Complemento a la conmutatividad y la asociatividad de la segunda operacin
+;;; Complemento a la conmutatividad y la asociatividad de la segunda operación
 
 ;;; NOTA:
 ;;;
-;;; Se aplican comentarios anlogos a los del caso anterior.
+;;; Se aplican comentarios análogos a los del caso anterior.
 
 ;; (defthm |a * (b * c) = b * (a * c)|
 ;;   (implies (and (coeficientep a) (coeficientep b) (coeficientep c))
@@ -770,7 +770,7 @@ To certify this book, first, create a wo
 	   :in-theory (disable |a + b = 0 <=> b = - a|)
 	   :use (:instance |a + b = 0 <=> b = - a| (a (- a)) (b a)))))
 
-;;; Distributividad de la inversa sobre la primera operacin
+;;; Distributividad de la inversa sobre la primera operación
 
 ;; (defthm |- (a + b) = (- a) + (- b)|
 ;;   (implies (and (coeficientep a) (coeficientep b))
@@ -788,7 +788,7 @@ To certify this book, first, create a wo
 	   :use (:instance |a + b = 0 <=> b = - a|
 			   (a (+ a b)) (b (+ (- a) (- b)))))))
 
-;;; Inverso del neutro de la primera operacin
+;;; Inverso del neutro de la primera operación
 
 ;; (defthm |- 0 = 0|
 ;;   (= (- (nulo)) (nulo))
@@ -802,7 +802,7 @@ To certify this book, first, create a wo
 	   :in-theory (disable |a + b = 0 <=> b = - a|)
 	   :use (:instance |a + b = 0 <=> b = - a| (a (0_f)) (b (0_f))))))
 
-;;; Generalizacin de |a + (- a) = 0|
+;;; Generalización de |a + (- a) = 0|
 
 ;; (defthm |a + ((- a) + b) = b|
 ;;   (implies (and (coeficientep a) (coeficientep b))
@@ -828,7 +828,7 @@ To certify this book, first, create a wo
 		(fdp (double-rewrite b)))
 	   (= (+ a (+ b (- a))) b)))
 
-;;; Elemento cancelador de la segunda operacin
+;;; Elemento cancelador de la segunda operación
 
 ;; (defthm |0 * a = 0|
 ;;   (implies (coeficientep a)
@@ -857,7 +857,7 @@ To certify this book, first, create a wo
   (implies (fdp (double-rewrite a))
 	   (= (* a (0_f)) (0_f))))
 
-;;; Extraccin del inverso
+;;; Extracción del inverso
 
 ;; (defthm |a * (- b) = - (a * b)|
 ;;   (implies (and (coeficientep a) (coeficientep b))
@@ -885,7 +885,7 @@ To certify this book, first, create a wo
 		(fdp (double-rewrite b)))
 	   (= (* (- a) b) (- (* a b)))))
 
-;;; Generalizacin de |- 0 = 0|
+;;; Generalización de |- 0 = 0|
 
 ;; (defthm |- a = 0 <=> a = 0|
 ;;   (implies (coeficientep a)
@@ -1027,10 +1027,10 @@ To certify this book, first, create a wo
 ;;; NOTA:
 ;;;
 ;;; El lado izquierdo puede aparecer por varias razones, sin
-;;; descartar una aplicacin de |- (a + b) = (- a) + (- b)| en un
+;;; descartar una aplicación de |- (a + b) = (- a) + (- b)| en un
 ;;; contexto en el que aparece |- (a + b) = c| y posteriormente se
-;;; establece que |c = 0|. Esto podra evitarse postponiendo la
-;;; definicin de dicha regla.
+;;; establece que |c = 0|. Esto podría evitarse postponiendo la
+;;; definición de dicha regla.
 
 ;; (defthm |(- a) + (- b) = 0 <=> a + b = 0|
 ;;   (implies (and (coeficientep a) (coeficientep b))
@@ -1049,7 +1049,7 @@ To certify this book, first, create a wo
 
 ;;; NOTA:
 ;;;
-;;; En un anillo el recproco no es, en general, cierto.
+;;; En un anillo el recíproco no es, en general, cierto.
 
 ;; (defthm |b + c = 0 => (a * b) + (a * c) = 0|
 ;;   (implies (and (coeficientep a) (coeficientep b) (coeficientep c)
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fucongruencias-producto.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fucongruencias-producto.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fucongruencias-producto.lisp
@@ -30,9 +30,9 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
-;;; Demostracin de las congruencias de la igualdad de polinomios con
+;;; Demostración de las congruencias de la igualdad de polinomios con
 ;;; el producto externo y el producto.
 ;;; -----------------------------------------------------------------
 #|
@@ -74,7 +74,7 @@ To certify this book, first, create a wo
 	      :load-compiled-file nil)
 
 ;;; --------------------------------------------------------
-;;; stas son las propiedades de "polinomio" que lo abstraen
+;;; Éstas son las propiedades de "polinomio" que lo abstraen
 ;;; --------------------------------------------------------
 
 (defthm |m +M p != 0|
@@ -92,7 +92,7 @@ To certify this book, first, create a wo
 	   (equal (resto (+M m p)) p)))
 
 ;;; ++++++++++++++++++++++++++
-;;; + Barrera de abstraccin +
+;;; + Barrera de abstracción +
 ;;; ++++++++++++++++++++++++++
 
 (in-theory (disable +M))
@@ -101,8 +101,8 @@ To certify this book, first, create a wo
 ;;; Distributividad del producto externo respecto a la suma externa
 ;;; ---------------------------------------------------------------
 
-;;; Propiedades sintcticas de la suma de monomio y polinomio y la
-;;; normalizacin.
+;;; Propiedades sintácticas de la suma de monomio y polinomio y la
+;;; normalización.
 
 ;; (defthm |fn(m +Mo fn(p)) = fn(m +Mo p)|
 ;;   (equal (fn (+-monomio m (fn p)))
@@ -124,7 +124,7 @@ To certify this book, first, create a wo
   :hints (("Subgoal *1/8"
 	   :in-theory (enable +M))))
 
-;;; Este es un caso particular de la definicin de "+-monomio".
+;;; Este es un caso particular de la definición de "+-monomio".
 
 (defthm |n +Mo p = p_p +M (n +Mo p_r)|
   (implies (and (monomiop (double-rewrite n))
@@ -135,9 +135,9 @@ To certify this book, first, create a wo
 		  (+M (primero p) (+-monomio n (resto p)))))
   :hints (("Goal" :do-not '(generalize))))
 
-;;; Esta propiedad sintctica establece la relacin entre La suma de
+;;; Esta propiedad sintáctica establece la relación entre La suma de
 ;;; monomios y polinomios, el constructor de los polinomios y la
-;;; funcin de normalizacin.
+;;; función de normalización.
 
 (defthm |m +Mo fn(p) = fn(m +M p)|
   (implies (and (monomiop (double-rewrite m))
@@ -150,14 +150,14 @@ To certify this book, first, create a wo
 
 ;;; NOTA:
 ;;;
-;;; Este teorema es tremendamente complicado. Ntese que la igualdad a
-;;; la que apela es sintctica. El problema es una explosin
-;;; combinatoria en el nmero de casos debido, principalmente, a la
-;;; gran cantidad de casos existente en la definicin de
+;;; Este teorema es tremendamente complicado. Nótese que la igualdad a
+;;; la que apela es sintáctica. El problema es una explosión
+;;; combinatoria en el número de casos debido, principalmente, a la
+;;; gran cantidad de casos existente en la definición de
 ;;; "+-monomio". Por otro lado, no parece factible simplificar dicha
-;;; definicin, ya que esto obligara a aadir hiptesis a muchos
+;;; definición, ya que esto obligaría a ańadir hipótesis a muchos
 ;;; teoremas que son necesarios para demostrar la congruencia
-;;; (recurdese que las congruencias son incondicionales). La
+;;; (recuérdese que las congruencias son incondicionales). La
 ;;; consecuencia es una prueba muy extensa, poco automatizada y muy
 ;;; sensible al entorno.
 
@@ -289,7 +289,7 @@ To certify this book, first, create a wo
 ;;;
 ;;; En realidad, este es el teorema que realmente queremos demostrar
 ;;; pero, para ello, hemos necesitado el anterior. Se emplea en la
-;;; demostracin de que "m *M p = m *M fn(p)", que permite establecer
+;;; demostración de que "m *M p = m *M fn(p)", que permite establecer
 ;;; la congruencia con el producto externo.
 
 (in-theory (disable |fn(m *M (n +Mo p)) =P fn((m * n) +Mo (m *M p))|))
@@ -306,7 +306,7 @@ To certify this book, first, create a wo
 ;; (in-theory (disable |fn(m *M (n +Mo p)) = fn((m * n) +Mo (m *M p))|))
 
 ;;; ++++++++++++++++++++++++++
-;;; + Barrera de abstraccin +
+;;; + Barrera de abstracción +
 ;;; ++++++++++++++++++++++++++
 
 (in-theory (disable = (=)))
@@ -315,7 +315,7 @@ To certify this book, first, create a wo
 ;;; Congruencias de la igualdad de polinomios con el producto externo
 ;;; -----------------------------------------------------------------
 
-;;; Primer parmetro
+;;; Primer parámetro
 
 ;; (defcong MON::= = (*-monomio m p) 1
 ;;   :hints (("Goal" :in-theory (enable MON::=))))
@@ -327,11 +327,11 @@ To certify this book, first, create a wo
 	      (*-monomio m2 p)))
   :rule-classes :congruence)
 
-;;; Segundo parmetro
+;;; Segundo parámetro
 
 ;;; NOTA:
 ;;;
-;;; Esta propiedad es expansiva; restringimos su aplicacin sintcticamente
+;;; Esta propiedad es expansiva; restringimos su aplicación sintácticamente
 
 (local
   (defthm |m +M p = m +Mo p|
@@ -383,7 +383,7 @@ To certify this book, first, create a wo
 ;;; Congruencia de la igualdad de polinomios con el producto
 ;;; --------------------------------------------------------
 
-;;; Segundo parmetro
+;;; Segundo parámetro
 
 (defthm |p * fn(q) = p * q|
   (= (* p (fn q)) (* p q)))
@@ -396,7 +396,7 @@ To certify this book, first, create a wo
 	      (* p q2)))
   :rule-classes :congruence)
 
-;;; Primer parmetro
+;;; Primer parámetro
 
 (defthm |fn(p) * q = p * q|
   (= (* (fn p) q) (* p q)))
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fucongruencias-suma.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fucongruencias-suma.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fucongruencias-suma.lisp
@@ -30,23 +30,23 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
-;;; Aqu se demuestran las congruencias de la igualdad de polinomios
+;;; Aquí se demuestran las congruencias de la igualdad de polinomios
 ;;; con la suma. Las demostraciones son complejas debido a que
 ;;; necesitan reglas expansivas. Estas reglas son peligrosas, ya que
-;;; pueden producir fcilmente ciclos en el demostrador. Para
-;;; restringir su aplicacin caben dos opciones:
+;;; pueden producir fácilmente ciclos en el demostrador. Para
+;;; restringir su aplicación caben dos opciones:
 ;;;
-;;; 1. Desactivarlas y usarlas explcitamente donde sea necesario. Una
+;;; 1. Desactivarlas y usarlas explícitamente donde sea necesario. Una
 ;;; variante es no generar la regla en absoluto (es decir, introducir
-;;; el teorema con la clases de reglas vaca).
+;;; el teorema con la clases de reglas vacía).
 ;;;
-;;; 2. Restringir su aplicacin sintcticamente para prevenir
+;;; 2. Restringir su aplicación sintácticamente para prevenir
 ;;; expansiones en cadena. Esto se puede lograr graciasa syntaxp.
 ;;;
-;;; Elegimos la segunda opcin porque se consigue un mayor grado de
-;;; automatizacin y hace a las demostraciones menos sensibles a los
+;;; Elegimos la segunda opción porque se consigue un mayor grado de
+;;; automatización y hace a las demostraciones menos sensibles a los
 ;;; cambios.
 ;;; ------------------------------------------------------------------
 #|
@@ -91,11 +91,11 @@ To certify this book, first, create a wo
 ;;; Congruencia de la igualdad de polinomios con la suma
 ;;; ----------------------------------------------------
 
-;;; Segundo parmetro
+;;; Segundo parámetro
 
 ;;; NOTA:
 ;;;
-;;; Esta propiedad es expansiva; restringimos su aplicacin sintcticamente
+;;; Esta propiedad es expansiva; restringimos su aplicación sintácticamente
 
 (defthm
   polinomiop-implies-true-listp
@@ -141,7 +141,7 @@ To certify this book, first, create a wo
 	      (+ p q2)))
   :rule-classes :congruence)
 
-;;; Primer parmetro
+;;; Primer parámetro
 
 ;; (defcong = = (+ p q) 1
 ;;   :hints (("Goal"
@@ -165,7 +165,7 @@ To certify this book, first, create a wo
 
 ;;; NOTA:
 ;;;
-;;; Esta propiedad es expansiva; restringimos su aplicacin sintcticamente
+;;; Esta propiedad es expansiva; restringimos su aplicación sintácticamente
 
 (defthm |p + q = fn(p) + q|
   (implies (syntaxp (not (and (consp p) (eq (primero p) 'fn))))
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuforma-normal.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuforma-normal.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuforma-normal.lisp
@@ -30,16 +30,16 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
-;;; Desarrollo de la funcin de normalizacin que permite reducir la
-;;; comprobacin de la igualdad semntica de dos polinomios a la de
-;;; una igualdad sintctica de sus formas normales. Se define primero
+;;; Desarrollo de la función de normalización que permite reducir la
+;;; comprobación de la igualdad semántica de dos polinomios a la de
+;;; una igualdad sintáctica de sus formas normales. Se define primero
 ;;; una suma externa de un monomio con un polinomio ordenado, teniendo
-;;; en cuenta una posible cancelacin. A partir de aqu se define la
-;;; forma normal y su relacin de equivalencia inducida. Se demuestran
+;;; en cuenta una posible cancelación. A partir de aquí se define la
+;;; forma normal y su relación de equivalencia inducida. Se demuestran
 ;;; algunas propiedades importantes como la idempotencia de la
-;;; normalizacin.
+;;; normalización.
 ;;; ------------------------------------------------------------------
 #|
 To certify this book, first, create a world with the following packages:
@@ -83,7 +83,7 @@ To certify this book, first, create a wo
 ;;; Polinomios ordenados
 ;;; --------------------
 
-;;; Esta funcin permite averiguar si un monomio debe preceder al
+;;; Esta función permite averiguar si un monomio debe preceder al
 ;;; monomio principal de un polinomio ordenado
 
 (defmacro termino-mayor-termino-principal (m p)
@@ -91,7 +91,7 @@ To certify this book, first, create a wo
        (FUTER::< (termino (primero ,p)) (termino ,m))))
 
 ;;; Reconocedor de polinomios estrictamente ordenado mediante un orden
-;;; de trminos decreciente y que no poseen monomios nulos
+;;; de términos decreciente y que no poseen monomios nulos
 
 (defun ordenadop (p)
   (and (polinomiop p)
@@ -101,7 +101,7 @@ To certify this book, first, create a wo
 		(ordenadop (resto p))))))
 
 ;;; ------------------------------------
-;;; Adicin de un monomio y un polinomio
+;;; Adición de un monomio y un polinomio
 ;;; ------------------------------------
 
 ;;; Suma un monomio a un polinomio
@@ -125,7 +125,7 @@ To certify this book, first, create a wo
 ;;; NOTA:
 ;;;
 ;;; Hay que garantizar (cosa que probaremos en breve) que si el
-;;; polinomio est normalizado, el resultado tambin.
+;;; polinomio está normalizado, el resultado también.
 
 ;; (defun +-monomio (m p)
 ;;   (cond ((and (not (monomiop m)) (not (polinomiop p)))
@@ -404,18 +404,18 @@ To certify this book, first, create a wo
 ;;; Forma normal
 ;;; ------------
 
-;;; Normalizacin de un polinomio meidante adicin de monomios.
+;;; Normalización de un polinomio meidante adición de monomios.
 
 ;;; NOTA:
 ;;;
-;;; Este es un punto en el que en un futuro se podra trabajar para
-;;; mejorar la eficiencia de los algoritmos. Bsicamente podemos
-;;; entender la normalizacin de un polinomio como un proceso de
-;;; ordenacin (con algunas diferencias importantes) y, con ste
-;;; smil, el algoritmo que se presenta a continuacin correspondera
-;;; con un mtodo directo (insercin directa). Cabra la posibilidad
-;;; de adaptar algoritmos de ordenacin ms eficientes (los de Hoare y
-;;; Williams seran buenas opciones) para normalizar polinomios.
+;;; Este es un punto en el que en un futuro se podría trabajar para
+;;; mejorar la eficiencia de los algoritmos. Básicamente podemos
+;;; entender la normalización de un polinomio como un proceso de
+;;; ordenación (con algunas diferencias importantes) y, con éste
+;;; símil, el algoritmo que se presenta a continuación correspondería
+;;; con un método directo (inserción directa). Cabría la posibilidad
+;;; de adaptar algoritmos de ordenación más eficientes (los de Hoare y
+;;; Williams serían buenas opciones) para normalizar polinomios.
 
 (defun fn (p)
   (cond ((or (not (polinomiop p)) (nulop p))
@@ -433,7 +433,7 @@ To certify this book, first, create a wo
 ;;;
 ;;; NOTA:
 ;;;
-;;; Un polinomio normalizado coincide sintcticamente con su forma
+;;; Un polinomio normalizado coincide sintácticamente con su forma
 ;;; normal.
 
 (defmacro fnp (p)
@@ -445,22 +445,22 @@ To certify this book, first, create a wo
   (ordenadop (fn p))
   :rule-classes (:type-prescription :rewrite))
 
-;;; Si un polinomio est ordenado entonces est en forma normal
+;;; Si un polinomio está ordenado entonces está en forma normal
 
 (defthm fn-ordenado
   (implies (ordenadop (double-rewrite p))
 	   (equal (fn p) p)))
 
-;;; Un polinomio est en forma normal si, y slo si, est ordenado
+;;; Un polinomio está en forma normal si, y sólo si, está ordenado
 
 ;;; NOTA:
 ;;;
-;;; Este teorema establece la correccin de la funcin de
-;;; normalizacin frente a la especificacin dada por el hecho de que
+;;; Este teorema establece la corrección de la función de
+;;; normalización frente a la especificación dada por el hecho de que
 ;;; un polinomio en forma normal debe tener sus monomios ordenados
 ;;; decrecientemente y no puede poseer monomios nulos. Al ser la
-;;; ordenacin estricta, se evita la posibilidad de que aparezcan
-;;; monomios con el mismo trmino.
+;;; ordenación estricta, se evita la posibilidad de que aparezcan
+;;; monomios con el mismo término.
 
 (defthm fnp-iff-ordenadop
   (iff (fnp p) (ordenadop p)))
@@ -472,15 +472,15 @@ To certify this book, first, create a wo
   (fnp (fn p)))
 
 ;;; ------------------
-;;; Igualdad semntica
+;;; Igualdad semántica
 ;;; ------------------
 
-;;; Igualdad semntica
+;;; Igualdad semántica
 
 ;;; NOTA:
 ;;;
-;;; Aqu radica una de las aplicaciones de la forma normal: permitir
-;;; comprobar si dos polinomios son iguales mdulo formas normales.
+;;; Aquí radica una de las aplicaciones de la forma normal: permitir
+;;; comprobar si dos polinomios son iguales módulo formas normales.
 
 ;; (defun = (p1 p2)
 ;;   (equal (fn p1) (fn p2)))
@@ -488,12 +488,12 @@ To certify this book, first, create a wo
 (defun = (p1 p2)
   (=P (fn p1) (fn p2)))
 
-;;; La igualdad semntica es una relacin de equivalencia
+;;; La igualdad semántica es una relación de equivalencia
 
 ;;; NOTA:
 ;;;
 ;;; Esto abre paso al establecimiento de las congruencias entre la
-;;; igualdad semntica y las operaciones.
+;;; igualdad semántica y las operaciones.
 
 (defthm
   =-is-an-equivalence
@@ -558,7 +558,7 @@ To certify this book, first, create a wo
 			   (FLD::a a) (FLD::b b)
 			   (FLD::c (coeficiente (primero p)))))))
 
-;; (defthm |(a + b) = 0 => a +Mo (b +Mo p) = (a + b) +Mo p|
+;; (defthm |Ź(a + b) = 0 => a +Mo (b +Mo p) = (a + b) +Mo p|
 ;;   (implies (and (COE::coeficientep a)
 ;; 		(COE::coeficientep b)
 ;; 		(TER::terminop te)
@@ -584,7 +584,7 @@ To certify this book, first, create a wo
 ;;; polinomio
 ;;; -----------------------------------------------------------------
 
-;;; Primer parmetro
+;;; Primer parámetro
 
 ;; (defcong MON::= = (+M m p) 1
 ;;   :hints (("Goal" :in-theory (enable MON::=))))
@@ -596,7 +596,7 @@ To certify this book, first, create a wo
 	      (+M m2 p)))
   :rule-classes :congruence)
 
-;;; Segundo parmetro
+;;; Segundo parámetro
 
 ;; (defcong = = (+M m p) 2)
 
@@ -624,7 +624,7 @@ To certify this book, first, create a wo
 ;;; Congruencia de la igualdad de polinomios con la suma externa
 ;;; ------------------------------------------------------------
 
-;;; Primer parmetro
+;;; Primer parámetro
 
 ;; (defcong MON::= equal (+-monomio m p) 1
 ;;   :hints (("Goal" :in-theory (enable MON::=))))
@@ -640,14 +640,14 @@ To certify this book, first, create a wo
 
 ;;; NOTA:
 ;;;
-;;; Esta propiedad es expansiva; restringimos su aplicacin sintcticamente
+;;; Esta propiedad es expansiva; restringimos su aplicación sintácticamente
 
 (local
   (defthm +-monomio-fn
     (implies (syntaxp (not (and (consp p) (eq (primero p) 'fn))))
 	     (= (+-monomio m p) (+-monomio m (fn p))))))
 
-;;; Segundo parmetro
+;;; Segundo parámetro
 
 ;; (defcong = = (+-monomio m p) 2)
 
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fumonomio.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fumonomio.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fumonomio.lisp
@@ -23,19 +23,19 @@
 
 ;;  Based on
 ;;; ------------------------------------------------------------------
-;;; Monomios con coeficientes y trminos abstractos
+;;; Monomios con coeficientes y términos abstractos
 ;;;
 ;;; Autores:
 ;;;
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
-;;; Pares coeficiente-trmino. Se define una igualdad semntica, ya
+;;; Pares coeficiente-término. Se define una igualdad semántica, ya
 ;;; que dos monomios con coeficiente nulo han de ser interpretados
-;;; como el mismo, aunque tengan distinto trmino. Orden de monomios
-;;; heredado de los trminos.
+;;; como el mismo, aunque tengan distinto término. Orden de monomios
+;;; heredado de los términos.
 ;;; ------------------------------------------------------------------
 #|
 To certify this book, first, create a world with the following packages:
@@ -131,7 +131,7 @@ To certify this book, first, create a wo
 (defun nulop (a)
   (FLD::= (coeficiente a) (FLD::0_f)))
 
-;;; Neutro de la operacin
+;;; Neutro de la operación
 
 ;; (defun identidad ()
 ;;   (monomio (COE::identidad) (TER::uno)))
@@ -139,7 +139,7 @@ To certify this book, first, create a wo
 (defun identidad ()
   (monomio (FLD::1_f) (FUTER::uno)))
 
-;;; Operacin
+;;; Operación
 
 ;; (defun * (a b)
 ;;   (monomio (COE::* (coeficiente a) (coeficiente b))
@@ -149,7 +149,7 @@ To certify this book, first, create a wo
   (monomio (FLD::* (coeficiente a) (coeficiente b))
 	   (FUTER::* (termino a) (termino b))))
 
-;;; Igualdad semntica
+;;; Igualdad semántica
 
 ;; (defun = (a b)
 ;;   (or (and (not (monomiop a)) (not (monomiop b)))
@@ -167,7 +167,7 @@ To certify this book, first, create a wo
 	   (FLD::= (coeficiente a) (coeficiente b))
 	   (FUTER::= (termino a) (termino b)))))
 
-;;; Igualdad de los trminos subyacentes
+;;; Igualdad de los términos subyacentes
 
 (defmacro =T (a b)
   `(FUTER::= (termino ,a) (termino ,b)))
@@ -177,13 +177,13 @@ To certify this book, first, create a wo
 (defmacro < (a b)
   `(FUTER::< (termino ,a) (termino ,b)))
 
-;;; Inmersin en los ordinales
+;;; Inmersión en los ordinales
 
 (defmacro monomio->ordinal (a)
   `(FUTER::termino->ordinal (termino ,a)))
 
 ;;; -----------------------
-;;; Teora de las funciones
+;;; Teoría de las funciones
 ;;; -----------------------
 
 (deftheory funciones
@@ -287,13 +287,13 @@ To certify this book, first, create a wo
 	      (* x y2)))
   :rule-classes :congruence)
 
-;;; Conmutatividad de la operacin
+;;; Conmutatividad de la operación
 
 (defthm |a * b = b * a|
   (implies (and (monomiop a) (monomiop b))
 	   (= (* a b) (* b a))))
 
-;;; Asociatividad de la operacin
+;;; Asociatividad de la operación
 
 ;; (defthm |(a * b) * c = a * (b * c)|
 ;;   (implies (and (monomiop a) (monomiop b) (monomiop c))
@@ -307,21 +307,21 @@ To certify this book, first, create a wo
   :hints (("Goal"
 	   :in-theory (disable (nulo) FLD::|a + b = b + a|))))
 
-;;; Neutro de la operacin
+;;; Neutro de la operación
 
 (defthm |1 * b = b|
   (implies (monomiop b)
 	   (= (* (identidad) b) b))
   :hints (("Goal" :in-theory (disable (identidad)))))
 
-;;; Cancelativo de la operacin
+;;; Cancelativo de la operación
 
 (defthm |a = 0 => a * b = 0|
   (implies (and (monomiop a) (monomiop b) (nulop a))
 	   (nulop (* a b)))
   :hints (("Goal" :in-theory (disable (nulo)))))
 
-;;; Coeficiente y trmino del constructor
+;;; Coeficiente y término del constructor
 
 ;; (defthm coeficiente-monomio
 ;;   (implies (and (coeficientep c) (terminop e))
@@ -339,14 +339,14 @@ To certify this book, first, create a wo
   (implies (and (fdp (double-rewrite c)) (terminop e))
 	   (FUTER::= (termino (monomio c e)) e)))
 
-;;; Eliminacin de destructores
+;;; Eliminación de destructores
 
 (defthm monomio-coeficiente-termino
   (implies (monomiop m)
 	   (equal (monomio (coeficiente m) (termino m)) m))
   :rule-classes (:rewrite :elim))
 
-;;; Coeficiente y trmino de la operacin
+;;; Coeficiente y término de la operación
 
 ;; (defthm coeficiente-*
 ;;   (COE::= (coeficiente (* a b))
@@ -362,7 +362,7 @@ To certify this book, first, create a wo
   (FUTER::= (termino (* a b))
 	    (FUTER::* (termino a) (termino b))))
 
-;;; Buena fundamentacin
+;;; Buena fundamentación
 
 (defthm buena-fundamentacion-<-M
   (and (implies (monomiop a)
@@ -437,7 +437,7 @@ To certify this book, first, create a wo
   (monomio (FLD::+ (coeficiente a) (coeficiente b))
 	   (termino a)))
 
-;;; Negacin
+;;; Negación
 
 ;; (defun - (a)
 ;;   (monomio (COE::- (coeficiente a)) (termino a)))
@@ -467,7 +467,7 @@ To certify this book, first, create a wo
   (implies (nulop a)
 	   (nulop (* b a))))
 
-;;; Complemento a la conmutatividad y la asociatividad de la operacin
+;;; Complemento a la conmutatividad y la asociatividad de la operación
 
 (defthm |a * (b * c) = b * (a * c)|
   (implies (and (monomiop a) (monomiop b) (monomiop c))
@@ -562,12 +562,12 @@ To certify this book, first, create a wo
 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 
 ;;; ++++++++++++++++++++++++++
-;;; + Barrera de abstraccin +
+;;; + Barrera de abstracción +
 ;;; ++++++++++++++++++++++++++
 
 ;;; NOTA:
 ;;;
-;;; A partir de aqu se proceder por aplicacin de las propiedades
+;;; A partir de aquí se procederá por aplicación de las propiedades
 
 (in-theory (disable funciones))
 (in-theory (enable nulop (nulop) (:type-prescription nulop)))
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuopuesto.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuopuesto.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuopuesto.lisp
@@ -30,13 +30,13 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
 ;;; Desarrollo del opuesto de un polinomio, que se define monomio a
-;;; monomio. Su correccin se prueba demostrando que la funcin que lo
-;;; calcula produce el inverso aditivo. Para que stas y otras
-;;; propiedades sean incondicionales (carezcan de hiptesis) se
-;;; completa cuidadosamente la definicin de la funcin. Se demuestra
+;;; monomio. Su corrección se prueba demostrando que la función que lo
+;;; calcula produce el inverso aditivo. Para que éstas y otras
+;;; propiedades sean incondicionales (carezcan de hipótesis) se
+;;; completa cuidadosamente la definición de la función. Se demuestra
 ;;; que los polinomios con las operaciones de suma y opuesto forman un
 ;;; grupo conmutativo.
 ;;; ------------------------------------------------------------------
@@ -82,8 +82,8 @@ To certify this book, first, create a wo
 ;;; Opuesto de polinomios
 ;;; ---------------------
 
-;;; La siguiente desactivacin es necesaria para la verificacin de la
-;;; proteccin del opuesto
+;;; La siguiente desactivación es necesaria para la verificación de la
+;;; protección del opuesto
 
 (in-theory (disable FUMON::monomio-coeficiente-termino))
 
@@ -191,7 +191,7 @@ To certify this book, first, create a wo
 (local (in-theory (disable polinomiop = + -)))
 
 ;;; -----------------------------------------------------------------------
-;;; El inverso debe ser invisible para la primera operacin y para s mismo
+;;; El inverso debe ser invisible para la primera operación y para sí mismo
 ;;; -----------------------------------------------------------------------
 (ACL2::set-invisible-fns-table ((+ -) (- -)))
 
@@ -245,7 +245,7 @@ To certify this book, first, create a wo
 	   :in-theory (disable |p + q = 0 <=> q = - p|)
 	   :use (:instance |p + q = 0 <=> q = - p| (p (- p)) (q p)))))
 
-;;; Distributividad de la inversa sobre la primera operacin
+;;; Distributividad de la inversa sobre la primera operación
 
 (defthm |- (p + q) = (- p) + (- q)|
   (= (- (+ p q)) (+ (- p) (- q)))
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fupolinomio-normalizado.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fupolinomio-normalizado.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fupolinomio-normalizado.lisp
@@ -30,11 +30,11 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
 ;;; Polinomios normalizados definidos a partir de los polinomios
-;;; desnormalizados y de la operacin de normalizacin. Ascenso de las
-;;; propiedades de anillo de la representacin desnormalizada a la
+;;; desnormalizados y de la operación de normalización. Ascenso de las
+;;; propiedades de anillo de la representación desnormalizada a la
 ;;; normalizada.
 ;;; ------------------------------------------------------------------
 #|
@@ -138,7 +138,7 @@ To certify this book, first, create a wo
   :rule-classes :type-prescription)
 
 ;;; --------------
-;;; Multiplicacin
+;;; Multiplicación
 ;;; --------------
 
 (defun * (p q)
@@ -386,13 +386,13 @@ To certify this book, first, create a wo
   (equal (- (nulo)) (nulo)))
 
 
-;;; Mejor con teoras
+;;; Mejor con teorías
 
 (in-theory (disable + (+) * (*) - (-) nulo (nulo) identidad (identidad)))
 
 (in-theory (disable = (=)))
 ;;; -----------------------------------------------------------------------
-;;; El inverso debe ser invisible para la primera operacin y para s mismo
+;;; El inverso debe ser invisible para la primera operación y para sí mismo
 ;;; -----------------------------------------------------------------------
 
 ;; (ACL2::set-invisible-fns-table ((+ -) (- -)))
@@ -432,7 +432,7 @@ To certify this book, first, create a wo
 (defthm |(p + q) * r = (p * r) + (q * r)|
   (= (* (+ p q) r) (+ (* p r) (* q r))))
 
-;;; Teorema de cancelacin
+;;; Teorema de cancelación
 
 ;; (defthm |p + r = q + r <=> p = q|
 ;;   (implies (and (polinomiop p) (polinomiop q))
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fupolinomio.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fupolinomio.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fupolinomio.lisp
@@ -29,11 +29,11 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
-;;; Representacin abstracta de los polinomios mediante listas propias
+;;; Representación abstracta de los polinomios mediante listas propias
 ;;; de ACL2 formadas por monomios que contienen coeficientes y
-;;; trminos abstractos.
+;;; términos abstractos.
 ;;; -------------------------------------------------------------------
 #|
 To certify this book, first, create a world with the following packages:
@@ -96,16 +96,16 @@ To certify this book, first, create a wo
 
 ;;; NOTA:
 ;;;
-;;; Posteriormente definiremos la igualdad semntica entre
-;;; polinomios. Entonces, esta definicin corresponder al
-;;; representante cannico de la clase de equivalencia formada por los
+;;; Posteriormente definiremos la igualdad semántica entre
+;;; polinomios. Entonces, esta definición corresponderá al
+;;; representante canónico de la clase de equivalencia formada por los
 ;;; polinomios nulos.
 
 (defmacro nulo () nil)
 
 ;;; NOTA:
 ;;;
-;;; La siguiente versin se emplea en los casos base de las funciones
+;;; La siguiente versión se emplea en los casos base de las funciones
 ;;; recursivas que trabajan con polinomios.
 
 (defmacro nulop (p)
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuproducto.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuproducto.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fuproducto.lisp
@@ -33,15 +33,15 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
 ;;; Desarrollo del producto externo de un monomio por un polinomio y
 ;;; del producto de polinomios. Las funciones se completan
 ;;; cuidadosamente, de lo contrario, no es posible establecer las
-;;; congruencias, ya que stas no pueden contener hiptesis. Se
+;;; congruencias, ya que éstas no pueden contener hipótesis. Se
 ;;; demuestra que los polinomios con el producto forman un monoide
 ;;; conmutativo y que el producto distribuye respecto de la suma,
-;;; completndose con esto la demostracin de las propiedades del
+;;; completándose con esto la demostración de las propiedades del
 ;;; anillo de polinomios.
 ;;; ----------------------------------------------------------------
 #|
@@ -130,12 +130,12 @@ To certify this book, first, create a wo
   (implies (polinomiop (double-rewrite p))
 	   (= (*-monomio (FUMON::identidad) p) p)))
 
-;;; Cancelacin
+;;; Cancelación
 
 ;;; NOTA:
 ;;;
-;;; Primero se demuestra sintcticamente, introduciendo la forma
-;;; normal. Luego se extiende a la igualdad semntica.
+;;; Primero se demuestra sintácticamente, introduciendo la forma
+;;; normal. Luego se extiende a la igualdad semántica.
 
 (defthm |m = 0 => fn(m *M p) =e 0|
   (implies (FUMON::nulop m)
@@ -163,7 +163,7 @@ To certify this book, first, create a wo
 ;;; NOTA:
 ;;;
 ;;; Esta propiedad permite cambiar un producto externo por otro
-;;; ms sencillo sobre monomios.
+;;; más sencillo sobre monomios.
 
 (defthm |m1 *M (m2 *M p) = (m1 * m2) *M p|
   (implies (and (monomiop (double-rewrite m1))
@@ -246,7 +246,7 @@ To certify this book, first, create a wo
 (defthm |1 * p = p|
   (= (* (identidad) p) p))
 
-;;; Cancelacin
+;;; Cancelación
 
 (defthm |0 * p =e 0|
   (equal (* (nulo) p) (nulo)))
@@ -264,8 +264,8 @@ To certify this book, first, create a wo
 
 ;;; NOTA:
 ;;;
-;;; La induccin apropiada es mltiple. Unas veces se requiere una
-;;; hiptesis de induccin sobre uno de los parmetros, otras veces
+;;; La inducción apropiada es múltiple. Unas veces se requiere una
+;;; hipótesis de inducción sobre uno de los parámetros, otras veces
 ;;; sobre el otro y otras sobre ambos. Hemos de suministrar el
 ;;; esquema.
 
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fusuma.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fusuma.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/fusuma.lisp
@@ -30,14 +30,14 @@
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
 ;;; Desarrollo de la suma de polinomios definida simplemente como la
-;;; concatenacin de las listas de monomios que los integran. Las
-;;; propiedades de la concatenacin de listas permiten establecer la
+;;; concatenación de las listas de monomios que los integran. Las
+;;; propiedades de la concatenación de listas permiten establecer la
 ;;; base para realizar demostraciones de propiedades sobre los
-;;; polinomios ms complicadas que incorporan la igualdad
-;;; semntica. Se demuestra que los polinomios con la operacin de
+;;; polinomios más complicadas que incorporan la igualdad
+;;; semántica. Se demuestra que los polinomios con la operación de
 ;;; suma forman un monoide conmutativo.
 ;;; ----------------------------------------------------------------
 #|
Index: acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/futermino.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/futermino.lisp
+++ acl2-8.4dfsg/books/workshops/2006/cowles-gamboa-euclid/Euclid/fld-u-poly/futermino.lisp
@@ -26,29 +26,29 @@
 
 ;;  Based on
 ;;; ------------------------------------------------------------------
-;;; Trminos abstractos
+;;; Términos abstractos
 ;;;
 ;;; Autores:
 ;;;
 ;;; Inmaculada Medina Bulo
 ;;; Francisco Palomo Lozano
 ;;;
-;;; Descripcin:
+;;; Descripción:
 ;;;
-;;; Un monoide conmutativo de trminos con un orden bien fundamentado
-;;; cuya representacin se abstrae mediante un encapsulado. Las listas
-;;; propias de nmeros naturales de ACL2 con la suma elemento a
-;;; elemento y el orden lexicogrfico sirven como modelo de la teora
-;;; generada. La buena fundamentacin del orden se establece por
-;;; inmersin en los ordinales ACL2.
+;;; Un monoide conmutativo de términos con un orden bien fundamentado
+;;; cuya representación se abstrae mediante un encapsulado. Las listas
+;;; propias de números naturales de ACL2 con la suma elemento a
+;;; elemento y el orden lexicográfico sirven como modelo de la teoría
+;;; generada. La buena fundamentación del orden se establece por
+;;; inmersión en los ordinales ACL2.
 ;;;
 ;;; Notas generales:
 ;;;
-;;; La parte ms complicada es la inmersin y la buena fundamentacin
+;;; La parte más complicada es la inmersión y la buena fundamentación
 ;;; del orden. Es curioso que los ordinales obtenidos son bastante
-;;; pequeos en relacin a, por ejemplo, los propuestos por Kaufmann,
-;;; Manolios y Moore como solucin al ejercicio 6.8 de su libro
-;;; Computer-Aided Reasoning. An Approach. Vase el trabajo
+;;; pequeńos en relación a, por ejemplo, los propuestos por Kaufmann,
+;;; Manolios y Moore como solución al ejercicio 6.8 de su libro
+;;; «Computer-Aided Reasoning. An Approach». Véase el trabajo
 ;;; presentado en Austin.
 ;;; ------------------------------------------------------------------
 #|
@@ -100,7 +100,7 @@ To certify this book, first, create a wo
   (and (integerp a)
        (>= a 0)))
 
-  ;;; Neutro de la operacin
+  ;;; Neutro de la operación
 
 ;;   (local
 ;;     (defun uno ()
@@ -112,7 +112,7 @@ To certify this book, first, create a wo
 (defun
   uno ()
   (hide 0))
-  ;;; Operacin
+  ;;; Operación
 
 ;;   (local
 ;;     (defun * (a b)
@@ -132,12 +132,12 @@ To certify this book, first, create a wo
   * (a b)
   (ACL2::+ a b))
 
-  ;;; Igualdad sintctica entre trminos
+  ;;; Igualdad sintáctica entre términos
 
 (defmacro = (a b)
   `(equal ,a ,b))
 
-  ;;; Inmersin en los ordinales
+  ;;; Inmersión en los ordinales
 
 ;;   (local
 ;;     (defun termino->e0-ordinal (a)
@@ -155,7 +155,7 @@ To certify this book, first, create a wo
   termino->ordinal (a)
   (ACL2::+ 1 a))
 
-  ;;; Orden lexicogrfico estricto
+  ;;; Orden lexicográfico estricto
 
 ;;   (local
 ;;     (defun < (a b)
@@ -178,7 +178,7 @@ To certify this book, first, create a wo
   ;;; Axiomas
   ;;; -------
 
-  ;;; El reconocedor es una funcin booleana
+  ;;; El reconocedor es una función booleana
 
 (defthm booleanp-terminop
   (booleanp (terminop a))
@@ -195,29 +195,29 @@ To certify this book, first, create a wo
   (terminop (uno))
   :rule-classes :type-prescription)
 
-  ;;; Conmutatividad de la operacin
+  ;;; Conmutatividad de la operación
 
 (defthm |a * b = b * a|
   (implies (and (terminop a) (terminop b))
 	   (= (* a b) (* b a))))
 
-  ;;; Asociatividad de la operacin
+  ;;; Asociatividad de la operación
 
 (defthm |(a * b) * c = a * (b * c)|
   (implies (and (terminop a) (terminop b) (terminop c))
 	   (= (* (* a b) c) (* a (* b c)))))
 
-  ;;; Neutro de la operacin
+  ;;; Neutro de la operación
 
 (defthm |1 * a = a|
   (implies (terminop a)
 	   (= (* (uno) a) a)))
 
   ;;; --------------------
-  ;;; Buena fundamentacin
+  ;;; Buena fundamentación
   ;;; --------------------
 
-  ;;; Extensin de la correccin de la inmersin
+  ;;; Extensión de la corrección de la inmersión
 
 ;;   (local
 ;;     (defthm extension-correccion
@@ -226,7 +226,7 @@ To certify this book, first, create a wo
 ;; 	       (o-p (termino->ordinal a)))
 ;;       :otf-flg t))
 
-  ;;; Correccin de la inmersin
+  ;;; Corrección de la inmersión
 
 ;;   (local
 ;;     (defthm o-p-termino->ordinal
@@ -235,12 +235,12 @@ To certify this book, first, create a wo
 ;;       :hints (("Goal"
 ;; 	       :in-theory (disable o-p termino->ordinal)))))
 
-  ;;; Buena fundamentacin
+  ;;; Buena fundamentación
 
   ;;; NOTA:
   ;;;
-  ;;; Este teorema es til como regla de reescritura para extender el
-  ;;; orden de trminos a polinomios.
+  ;;; Este teorema es útil como regla de reescritura para extender el
+  ;;; orden de términos a polinomios.
 
 (defthm buena-fundamentacion-<
   (and (implies (terminop a)
@@ -250,11 +250,11 @@ To certify this book, first, create a wo
 		(o< (termino->ordinal a) (termino->ordinal b))))
   :rule-classes (:rewrite :well-founded-relation))
 
-  ;;; La inmersin no produce 0
+  ;;; La inmersión no produce 0
 
   ;;; NOTA:
   ;;;
-  ;;; Estos teoremas facilitan la extensin del orden de trminos a
+  ;;; Estos teoremas facilitan la extensión del orden de términos a
   ;;; polinomios.
 
 (defthm |~(termino->ordinal(a) = 0)|
@@ -272,13 +272,13 @@ To certify this book, first, create a wo
   ;;; NOTA:
   ;;;
   ;;; En realidad estas propiedades no son independientes de los
-  ;;; axiomas. Se podran deducir de la inmersin.
+  ;;; axiomas. Se podrían deducir de la inmersión.
 
   ;;; Irreflexividad
 
 (defthm |~(a < a)|
   (not (< a a)))
-  ;;; Antisimetra
+  ;;; Antisimetría
 
 (defthm |a < b => ~(b < a)|
   (implies (< a b) (not (< b a))))
@@ -288,7 +288,7 @@ To certify this book, first, create a wo
 (defthm |a < b & b < c => a < c|
   (implies (and (< a b) (< b c)) (< a c)))
 
-  ;;; Tricotoma
+  ;;; Tricotomía
 
 (defthm |a < b or b < a or a = b|
   (implies (and (terminop a) (terminop b))
@@ -324,7 +324,7 @@ To certify this book, first, create a wo
   (implies (terminop a)
 	   (= (* a (uno)) a)))
 
-;;; Complemento a la conmutatividad y la asociatividad de la operacin
+;;; Complemento a la conmutatividad y la asociatividad de la operación
 
 (defthm |a * (b * c) = b * (a * c)|
   (implies (and (terminop a) (terminop b) (terminop c))
Index: acl2-8.4dfsg/books/workshops/2007/cowles-et-al/support/greve/ack.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2007/cowles-et-al/support/greve/ack.lisp
+++ acl2-8.4dfsg/books/workshops/2007/cowles-et-al/support/greve/ack.lisp
@@ -1,6 +1,6 @@
 #|-*-Lisp-*-=================================================================|#
 #|                                                                           |#
-#|      Copyright  2005-7 Rockwell Collins, Inc.  All Rights Reserved.      |#
+#|      Copyright © 2005-7 Rockwell Collins, Inc.  All Rights Reserved.      |#
 #|                                                                           |#
 #|===========================================================================|#
 (in-package "ACL2")
Index: acl2-8.4dfsg/books/workshops/2007/cowles-et-al/support/greve/defminterm.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2007/cowles-et-al/support/greve/defminterm.lisp
+++ acl2-8.4dfsg/books/workshops/2007/cowles-et-al/support/greve/defminterm.lisp
@@ -1,6 +1,6 @@
 #|-*-Lisp-*-=================================================================|#
 #|                                                                           |#
-#|      Copyright  2005-7 Rockwell Collins, Inc.  All Rights Reserved.      |#
+#|      Copyright © 2005-7 Rockwell Collins, Inc.  All Rights Reserved.      |#
 #|                                                                           |#
 #|===========================================================================|#
 (in-package "ACL2")
Index: acl2-8.4dfsg/books/workshops/2007/cowles-et-al/support/greve/defxch.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2007/cowles-et-al/support/greve/defxch.lisp
+++ acl2-8.4dfsg/books/workshops/2007/cowles-et-al/support/greve/defxch.lisp
@@ -1,6 +1,6 @@
 #|-*-Lisp-*-=================================================================|#
 #|                                                                           |#
-#|      Copyright  2005-7 Rockwell Collins, Inc.  All Rights Reserved.      |#
+#|      Copyright © 2005-7 Rockwell Collins, Inc.  All Rights Reserved.      |#
 #|                                                                           |#
 #|===========================================================================|#
 (in-package "ACL2")
Index: acl2-8.4dfsg/books/workshops/2007/rubio/support/abstract-reductions/confluence.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2007/rubio/support/abstract-reductions/confluence.lisp
+++ acl2-8.4dfsg/books/workshops/2007/rubio/support/abstract-reductions/confluence.lisp
@@ -216,7 +216,7 @@
 			(equiv-p z y p2))))))
 
 ;;; 1.2.1. equiv-p is an equivalence relation
-;;; 
+;;; ·········································
 
 ;;; The properties of equivalence relations (in q) are met by equiv-p:
 
@@ -241,7 +241,7 @@
 
 
 ;;; 1.2.2. equiv-p contains the reduction relation
-;;; 
+;;; ··············································
 
 (defthm equiv-p-contains-reduction
   (implies (and (q x)
@@ -258,7 +258,7 @@
 
 ;;; 1.2.3. equiv-p is the least equivalence relation with the above
 ;;; properties
-;;; 
+;;; ································································
 
 ;;; Let us assume that we have a relation eqv of equivalence in the set
 ;;; defined by q, containing the reduction steps, and let us show that
@@ -401,9 +401,9 @@
 (defun r-equiv (x y)
   (equal (normal-form x) (normal-form y)))
 
-;;; 
+;;; ············································································
 ;;; 2.2.1 Completeness
-;;; 
+;;; ············································································
 
 ;;; We want to show that if (equiv-p x y p) the the normal forms of x
 ;;; and y are the same. The idea is the following: if we have a proof
@@ -471,9 +471,9 @@
 			 (p (make-proof-between-normal-forms x y p)))))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.2.1 Soundness
-;;; 
+;;; ············································································
 
 ;;; We want to prove that if x and y have common normal forms then there
 ;;; is a proof between x and y.
Index: acl2-8.4dfsg/books/workshops/2007/rubio/support/abstract-reductions/convergent.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2007/rubio/support/abstract-reductions/convergent.lisp
+++ acl2-8.4dfsg/books/workshops/2007/rubio/support/abstract-reductions/convergent.lisp
@@ -304,7 +304,7 @@
 ;;; See newman.lisp for details.
 
 ;;; Well-founded multiset extension of rel
-;;; 
+;;; ······································
 
 ;(acl2::defmul-components rel)
 ;The list of components is:
@@ -314,7 +314,7 @@
 
 
 ;;; Auxiliary functions in the definition of transform-to-valley
-;;; 
+;;; ····························································
 
 (local
  (defun exists-local-peak (p)
@@ -356,7 +356,7 @@
 
 
 ;;; transform-to-valley terminates
-;;; 
+;;; ······························
 
 ;;; By functional instantiation of the same result in newman.lisp
 
@@ -392,7 +392,7 @@
 
 
 ;;; Definition of transform-to-valley
-;;; 
+;;; ·································
 (local
  (defun transform-to-valley (p)
    (declare (xargs :measure (if (steps-q p) (proof-measure p) nil)
@@ -404,7 +404,7 @@
 
 
 ;;; Properties of transform-to-valley: the Church-Rosser property
-;;; 
+;;; ·····························································
 
 ;;; By functional instantiation of the same results in newman.lisp
 
@@ -453,7 +453,7 @@
 ;;; w.r.t. it).
 
 ;;; Definition of proof-irreducible
-;;; 
+;;; ·······························
 
 ;;; REMARK: Iteratively apply reduction steps until an irreducible
 ;;; element is found, and collect all those proof steps.
@@ -490,7 +490,7 @@
 
 
 ;;; Main property of proof-irreducible (normalizing property)
-;;; 
+;;; ·························································
 
 ;;; REMARK: This is the assumed property of proof-irreducible in
 ;;; confluence.lisp.
@@ -566,7 +566,7 @@
 
 
 ;;; This is the same function as r-equiv in confluence.lisp
-;;; 
+;;; ·······················································
 
 ;;; REMARK: normal-form-aux is analogue NWM::normal-form, but
 ;;; normal-form is more "eficcient". The same for r-equiv.
@@ -592,7 +592,7 @@
 ;;; ----------------------------------------------------------------------------
 
 ;;; Completeness
-;;; 
+;;; ············
 
 ;;; By functional instantiation of the same results in confluence.lisp
 
@@ -612,7 +612,7 @@
 
 
 ;;; Soundness
-;;; 
+;;; ·········
 
 ;;; By functional instantiation of the same results in confluence.lisp
 
Index: acl2-8.4dfsg/books/workshops/2007/rubio/support/abstract-reductions/newman.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2007/rubio/support/abstract-reductions/newman.lisp
+++ acl2-8.4dfsg/books/workshops/2007/rubio/support/abstract-reductions/newman.lisp
@@ -165,7 +165,7 @@
 
 ;;; A first theorem: irreflexivity of rel
 
-;; Aadido para la 2.8
+;; Ańadido para la 2.8
 (defthm o<-irreflexive
   (not (o< x x)))
 
@@ -399,9 +399,9 @@
 
 ;;; In the sequel, we build a collection of rules to prove these two goals.
 
-;;; 
+;;; ············································································
 ;;; 3.2.1 Removing initial and final common parts
-;;; 
+;;; ············································································
 
 
 (local
@@ -474,9 +474,9 @@
 
 
 
-;;; 
+;;; ············································································
 ;;; 3.2.2 Removing the first element of the local peak
-;;; 
+;;; ············································································
 
 ;;; First, let's prove that the local peak and the transformed are
 ;;; proofs with the same endpoints, so their proof measures have the
@@ -611,13 +611,13 @@
 ;;;         (CDR (PROOF-MEASURE (TRANSFORM-LOCAL-PEAK (LOCAL-PEAK P))))))).
 
 
-;;; 
+;;; ············································································
 ;;; 3.2.3 An explicit reference to the peak-element
-;;; 
+;;; ············································································
 
 
 ;;; Definition and properties of peak-element
-;;; 
+;;; ·········································
 
 ;;; See the definition in abstract-proofs.lisp
 
@@ -675,13 +675,13 @@
 ;;;           (CDR (PROOF-MEASURE (TRANSFORM-LOCAL-PEAK (LOCAL-PEAK P))))))).
 
 
-;;; 
+;;; ············································································
 ;;; 3.2.4 The peak element is bigger than any element of
 ;;; (transform-local-peak (local-peak p))
-;;; 
+;;; ············································································
 
 ;;; Definition of being bigger (w.r.t rel) than every element of a list
-;;; 
+;;; ···································································
 
 (local
  (defun rel-bigger-than-list (x l)
@@ -693,7 +693,7 @@
 ;;; Conditions assuring that an element m is rel-bigger-than-list than
 ;;; the elements of the proof-measure of a proof, when the proof is,
 ;;; respectively, steps-up or steps-down:
-;;; 
+;;; ···································································
 
 ;;; A previous lemma: transitivity of rel is needed here
 
@@ -737,7 +737,7 @@
 ;;; (transform-local-peak (local-peak p)) in two proofs: the proof
 ;;; before the valley (steps-up) and the proof after the valley
 ;;; (steps-down). The following lemmas are needed for that purpose.
-;;; 
+;;; ····································································
 
 ;;; If p is a proof, so they are the proofs after and before the
 ;;; valley.
@@ -766,7 +766,7 @@
 
 
 ;;; The transformed proof is a valley
-;;; 
+;;; ·································
 
 (local
  (defthm local-peak-local-peak-p
@@ -791,7 +791,7 @@
 ;;; steps-up-proof-measure-w-f-v (and then prove that the peak-element
 ;;; is bigger than every element of the complexities of the
 ;;; proof-after-valley and the proof-before-valley, respectively.
-;;; 
+;;; ····································································
 
 
 
@@ -818,7 +818,7 @@
 
 
 ;;; Some technical lemmas
-;;; 
+;;; ·····················
 
 (local
  (defthm consp-proof-after-proof-instance
@@ -834,7 +834,7 @@
 
 
 ;;; And finally, the intended lemma
-;;; 
+;;; ·······························
 
 (local
  (defthm valley-rel-bigger-peak-lemma
@@ -847,9 +847,9 @@
                                     (transform-local-peak (local-peak p))))))))
 
 
-;;; 
+;;; ············································································
 ;;; 3.2.5 Using valley-rel-bigger-peak-lemma to simplify the goals
-;;; 
+;;; ············································································
 
 ;;; The two unresolved goals, as stated at the end of 3.2.3, can be
 ;;; simplified to t by using the previously proved
@@ -860,7 +860,7 @@
 ;;; following lemma (stating that the peak-element is not a member of
 ;;; the proof-meassure of the transformed proof),
 ;;; the calls to multiset-diff in the goals now disappear.
-;;; 
+;;; ···································································
 
 (local
  (encapsulate
@@ -897,7 +897,7 @@
 ;;; in the unresolved goal above, is reduced to a call to
 ;;; rel-bigger-than-list (and then valley-rel-bigger-peak-lemma will be
 ;;; applied)
-;;; 
+;;; ···································································
 
 
 (local
@@ -914,18 +914,18 @@
 ;;; With this two rules altogether with valley-rel-bigger-peak-lemma our
 ;;; unresolved goal becomes T, so we have:
 
-;;; 
+;;; ············································································
 ;;; 3.2.6  The main lemma of this book
-;;; 
+;;; ············································································
 
 (defthm transform-to-valley-admission
   (implies (exists-local-peak p)
 	   (mul-rel (proof-measure (replace-local-peak p))
 		    (proof-measure p))))
 
-;;; 
+;;; ············································································
 ;;; 3.2.7  Some final technical events
-;;; 
+;;; ············································································
 
 ;;; Needed in the admission proof of transform-to-valley
 
@@ -967,13 +967,13 @@
 ;;; 4.1 Some previous events
 ;;; ----------------------------------------------------------------------------
 
-;;; 
+;;; ·············································································
 ;;; 4.1.1 Previous rules needed to show that (transform-to-valley p) is eqv. to p
-;;; 
+;;; ·············································································
 
 
 ;;; We have to see that (replace-local-peak p) is equivalent to p
-;;; 
+;;; ·····························································
 
 ;;; An useful rule to deal with concatenation of proofs
 (local
@@ -1037,9 +1037,9 @@
 ;;; three pieces of p (before, at and after the peak), using the
 ;;; previous bridge lemma.
 
-;;; 
+;;; ·············································································
 ;;; 4.1.2 A rule needed to show that (transform-to-valley p) is a valley
-;;; 
+;;; ·············································································
 
 
 
@@ -1050,9 +1050,9 @@
    (implies (equiv-p x y p)
             (equal  (steps-valley p) (not (exists-local-peak p))))))
 
-;;; 
+;;; ·············································································
 ;;; 4.1.3 If equiv-p, then steps-q
-;;; 
+;;; ·············································································
 
 (local
  (defthm equiv-p-implies-stetps-q
@@ -1060,9 +1060,9 @@
 	    (steps-q p))
    :rule-classes :forward-chaining))
 
-;;; 
+;;; ·············································································
 ;;; 4.1.4 Disabling the induction rule for equiv-p
-;;; 
+;;; ·············································································
 
 
 (local (in-theory (disable equiv-p-induct)))
@@ -1079,7 +1079,7 @@
 
 
 ;;; It returns an equivalent proof
-;;; 
+;;; ······························
 
 
 (defthm equiv-p-x-y-transform-to-valley
@@ -1090,7 +1090,7 @@
 
 
 ;;; It returns a valley proof
-;;; 
+;;; ·························
 
 
 (defthm valley-transform-to-valley
Index: acl2-8.4dfsg/books/workshops/2007/rubio/support/multisets/multiset.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2007/rubio/support/multisets/multiset.lisp
+++ acl2-8.4dfsg/books/workshops/2007/rubio/support/multisets/multiset.lisp
@@ -12,7 +12,7 @@
 			(union-eq
 			 *common-lisp-symbols-from-main-lisp-package*
 			 '(remove-one multiset-diff ctoa atoc))))
-;;; Con la nueva representacin, aadimos ctoa y atoc al paquete MUL
+;;; Con la nueva representación, ańadimos ctoa y atoc al paquete MUL
 
 (certify-book "multiset" 1)
 
@@ -340,7 +340,7 @@
 
 
 ;;; Conviene tenerlo separado, por que hace falta. PERO NO DENTRO DEL
-;;; ENCAPSULADO. Como alternativa, yo la he puesto adems como regla de
+;;; ENCAPSULADO. Como alternativa, yo la he puesto además como regla de
 ;;; reescritura. Preguntar a CK si esto afecta a defmul.
 
 
@@ -348,9 +348,9 @@
 ;;; values must be greater than 0.  Thus, we define a new measure
 ;;; function "fn1" equal to "fn" except for integers, where 1 is added.
 
-;;; Nota: hace falta probar que la relacin es b.f. "respecto" a
+;;; Nota: hace falta probar que la relación es b.f. "respecto" a
 ;;; e0-ordinalp, porque la prueba esta hecha para los ordinales
-;;; antiguos. As que ahora tambin introducimos "ctoa"
+;;; antiguos. Así que ahora también introducimos "ctoa"
 
 (defun add1-if-integer (x)
   (if (integerp x) (1+ x) x))
@@ -414,10 +414,10 @@
 ;;; - The embedding justifying well-foundedness: mp-fn-o-p.
 
 ;;; Como originalmente hicimos la prueba con e0-ordinal, habiamos construido una
-;;; inmersin en los ordinales, llamada map-fn-e0-ordinal y toda la
-;;; prueba la habamos hecho probando que era una inmersin en los
+;;; inmersión en los ordinales, llamada map-fn-e0-ordinal y toda la
+;;; prueba la habíamos hecho probando que era una inmersión en los
 ;;; e0 ordinales. Para aprovechar eso en la 2-8, definimos map-fn-o-p
-;;; simplemente aplicando atoc en un ltimo paso.
+;;; simplemente aplicando atoc en un último paso.
 
 ;;; Measure property
 
@@ -457,9 +457,9 @@
 		       (map-fn-e0-ord (cdr l)))
       0))
 
-;;; Nuevo para la 2.8: m adelante tendremos que definir esto y
+;;; Nuevo para la 2.8: má adelante tendremos que definir esto y
 ;;; demostrar que se trata de una inmersion en los nuevos ordinales de
-;;; la versin 2.8:
+;;; la versión 2.8:
 ;; (defun map-fn-o-p (x)
 ;;   (declare (xargs :guard (mp-true-listp x)))
 ;;   (atoc (map-fn-e0-ord x)))
@@ -557,9 +557,9 @@
 ;;;    (e0-ord-< (map-fn-e0-ord n) (map-fn-e0-ord m))
 
 
-;;; 
+;;; ············································································
 ;;; 2.5.1 The measure is an e0-ordinal.
-;;; 
+;;; ············································································
 
 (local
  (defthm e0-ordinalp-insert-e0-ord-<
@@ -575,9 +575,9 @@
 	    (e0-ordinalp (map-fn-e0-ord m)))))
 
 
-;;; 
+;;; ············································································
 ;;; 2.5.2 The measure is an embedding
-;;; 
+;;; ············································································
 
 
 
@@ -611,7 +611,7 @@
 
 
 ;;; max-fn1-list (an element in l with maximal (fn1 ..)) and properties.
-;;; 
+;;; ······································································
 
 (local
  (defun max-fn1-list (l)
@@ -650,7 +650,7 @@
 
 
 ;;; An "alternative definition" of "map-fn-e0-ord".
-;;; 
+;;; ···············································
 
 (local
  (encapsulate
@@ -777,7 +777,7 @@
 
 
 ;;; Needed for forall-exists-rel-bigger-max-fn1-list
-;;; 
+;;; ················································
 
 ;;; We prove forall-exists-rel-bigger-max-fn1-list-lemma, establishing
 ;;; that if (mul-rel n m), and x is in n and not in m, then (fn1 x) is
@@ -873,7 +873,7 @@
 
 
 ;;; Previous lemmas to map-fn-e0-ord-measure, handling every subgoal
-;;; 
+;;; ································································
 
 ;;; Needed for "Subgoal *1/8":
 
@@ -955,7 +955,7 @@
 
 
 ;;; At last: map-fn-e0-ord-measure.
-;;; 
+;;; ·······························
 
 (local
  (encapsulate
@@ -1010,9 +1010,9 @@
 
 
 ;;; Pero con los nuevos ordinales no nos basta con esto, hay que demostrar
-;;; una inmersin en los ordinales con la nueva representacin. Esta
-;;; inmersin la d map-fn-o-p, definida simplemente
-;;; como la aplicacin de atoc a map-fn-e0-ord
+;;; una inmersión en los ordinales con la nueva representación. Esta
+;;; inmersión la dá map-fn-o-p, definida simplemente
+;;; como la aplicación de atoc a map-fn-e0-ord
 
 
 (defun map-fn-o-p (x)
Index: acl2-8.4dfsg/books/workshops/2007/rubio/support/simplicial-topology/generate-degenerate.lisp
===================================================================
--- acl2-8.4dfsg.orig/books/workshops/2007/rubio/support/simplicial-topology/generate-degenerate.lisp
+++ acl2-8.4dfsg/books/workshops/2007/rubio/support/simplicial-topology/generate-degenerate.lisp
@@ -2,7 +2,7 @@
 ;;; An elementary example about simplicial topology
 ;;; Supporting material for the paper "Formalizing simplicial topology
 ;;; in ACL2"
-;;; Authors: J.L. Ruiz-Reina, J. Rubio, M. Andrs, L. Lambn
+;;; Authors: J.L. Ruiz-Reina, J. Rubio, M. Andrés, L. Lambán
 ;;; Created: July, 2007
 ;;; Last modified: July 9th, 2007
 ;;; ==========================================================
