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• Instr

Instr-equiv

Basic equivalence relation for instr structures.

Definitions and Theorems

Function: instr-equiv$inline

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

Theorem: instr-equiv-is-an-equivalence

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

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

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

Theorem: instr-fix-under-instr-equiv

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

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

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

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

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

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

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

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

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