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• Modnamelist

Modnamelist-equiv

Basic equivalence relation for modnamelist structures.

Definitions and Theorems

Function: modnamelist-equiv$inline

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

Theorem: modnamelist-equiv-is-an-equivalence

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

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

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

Theorem: modnamelist-fix-under-modnamelist-equiv

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

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

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

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

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

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

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

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

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