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Escape

Escape-equiv

Basic equivalence relation for escape structures.

Definitions and Theorems

Function: escape-equiv$inline

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

Theorem: escape-equiv-is-an-equivalence

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

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

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

Theorem: escape-fix-under-escape-equiv

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

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

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

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

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

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

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

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

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