		Search-engine friendly clone of the ACL2 documentation.

Modscope

Modscope-equiv

Basic equivalence relation for modscope structures.

Definitions and Theorems

Function: modscope-equiv$inline

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

Theorem: modscope-equiv-is-an-equivalence

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

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

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

Theorem: modscope-fix-under-modscope-equiv

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

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

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

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

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

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

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

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

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