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Instruction

Instruction-equiv

Basic equivalence relation for instruction structures.

Definitions and Theorems

Function: instruction-equiv$inline

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

Theorem: instruction-equiv-is-an-equivalence

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

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

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

Theorem: instruction-fix-under-instruction-equiv

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

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

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

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

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

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

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

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

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