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Constraintlist

Constraintlist-equiv

Basic equivalence relation for constraintlist structures.

Definitions and Theorems

Function: constraintlist-equiv$inline

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

Theorem: constraintlist-equiv-is-an-equivalence

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

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

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

Theorem: constraintlist-fix-under-constraintlist-equiv

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

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

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

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

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

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

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

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

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