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• Escape-sequence

Escape-sequence-equiv

Basic equivalence relation for escape-sequence structures.

Definitions and Theorems

Function: escape-sequence-equiv$inline

(defun escape-sequence-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (escape-sequence-p acl2::x)
                              (escape-sequence-p acl2::y))))
  (equal (escape-sequence-fix acl2::x)
         (escape-sequence-fix acl2::y)))

Theorem: escape-sequence-equiv-is-an-equivalence

(defthm escape-sequence-equiv-is-an-equivalence
  (and (booleanp (escape-sequence-equiv x y))
       (escape-sequence-equiv x x)
       (implies (escape-sequence-equiv x y)
                (escape-sequence-equiv y x))
       (implies (and (escape-sequence-equiv x y)
                     (escape-sequence-equiv y z))
                (escape-sequence-equiv x z)))
  :rule-classes (:equivalence))

Theorem: escape-sequence-equiv-implies-equal-escape-sequence-fix-1

(defthm escape-sequence-equiv-implies-equal-escape-sequence-fix-1
  (implies (escape-sequence-equiv acl2::x x-equiv)
           (equal (escape-sequence-fix acl2::x)
                  (escape-sequence-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: escape-sequence-fix-under-escape-sequence-equiv

(defthm escape-sequence-fix-under-escape-sequence-equiv
  (escape-sequence-equiv (escape-sequence-fix acl2::x)
                         acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-escape-sequence-fix-1-forward-to-escape-sequence-equiv

(defthm
    equal-of-escape-sequence-fix-1-forward-to-escape-sequence-equiv
  (implies (equal (escape-sequence-fix acl2::x)
                  acl2::y)
           (escape-sequence-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-escape-sequence-fix-2-forward-to-escape-sequence-equiv

(defthm
    equal-of-escape-sequence-fix-2-forward-to-escape-sequence-equiv
  (implies (equal acl2::x (escape-sequence-fix acl2::y))
           (escape-sequence-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: escape-sequence-equiv-of-escape-sequence-fix-1-forward

(defthm escape-sequence-equiv-of-escape-sequence-fix-1-forward
  (implies (escape-sequence-equiv (escape-sequence-fix acl2::x)
                                  acl2::y)
           (escape-sequence-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: escape-sequence-equiv-of-escape-sequence-fix-2-forward

(defthm escape-sequence-equiv-of-escape-sequence-fix-2-forward
  (implies
       (escape-sequence-equiv acl2::x (escape-sequence-fix acl2::y))
       (escape-sequence-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)