		Search-engine friendly clone of the ACL2 documentation.

Snippet-mismatch

Snippet-mismatch-equiv

Basic equivalence relation for snippet-mismatch structures.

Definitions and Theorems

Function: snippet-mismatch-equiv$inline

(defun snippet-mismatch-equiv$inline (x y)
  (declare (xargs :guard (and (snippet-mismatch-p x)
                              (snippet-mismatch-p y))))
  (equal (snippet-mismatch-fix x)
         (snippet-mismatch-fix y)))

Theorem: snippet-mismatch-equiv-is-an-equivalence

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

Theorem: snippet-mismatch-equiv-implies-equal-snippet-mismatch-fix-1

(defthm snippet-mismatch-equiv-implies-equal-snippet-mismatch-fix-1
  (implies (snippet-mismatch-equiv x x-equiv)
           (equal (snippet-mismatch-fix x)
                  (snippet-mismatch-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: snippet-mismatch-fix-under-snippet-mismatch-equiv

(defthm snippet-mismatch-fix-under-snippet-mismatch-equiv
  (snippet-mismatch-equiv (snippet-mismatch-fix x)
                          x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-snippet-mismatch-fix-1-forward-to-snippet-mismatch-equiv

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

Theorem: equal-of-snippet-mismatch-fix-2-forward-to-snippet-mismatch-equiv

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

Theorem: snippet-mismatch-equiv-of-snippet-mismatch-fix-1-forward

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

Theorem: snippet-mismatch-equiv-of-snippet-mismatch-fix-2-forward

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