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• Inst

Inst-equiv

Basic equivalence relation for inst structures.

Definitions and Theorems

Function: inst-equiv$inline

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

Theorem: inst-equiv-is-an-equivalence

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

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

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

Theorem: inst-fix-under-inst-equiv

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

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

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

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

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

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

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

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

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