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• Combinational-type

Ctype-equiv

Equivalence relation for combinational-type keywords.

Signature

(ctype-equiv x y) → bool

Definitions and Theorems

Function: ctype-equiv

(defun ctype-equiv (x y)
  (declare (xargs :guard t))
  (let ((__function__ 'ctype-equiv))
    (declare (ignorable __function__))
    (equal (ctype-fix x) (ctype-fix y))))

Theorem: ctype-equiv-is-an-equivalence

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

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

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

Theorem: ctype-fix-under-ctype-equiv

(defthm ctype-fix-under-ctype-equiv
  (ctype-equiv (ctype-fix x) x))