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Opcode

Opcode-equiv

Basic equivalence relation for opcode structures.

Definitions and Theorems

Function: opcode-equiv$inline

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

Theorem: opcode-equiv-is-an-equivalence

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

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

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

Theorem: opcode-fix-under-opcode-equiv

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

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

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

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

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

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

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

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

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