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Symbol-equiv

(symbol-equiv x y) recognizes symbols that are identical under symbol-fix.

Definitions and Theorems

Function: symbol-equiv$inline

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

Theorem: symbol-equiv-is-an-equivalence

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

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

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

Theorem: symbol-fix-under-symbol-equiv

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

Theorem: symbol-equiv-implies-equal-symbol-name-1

(defthm symbol-equiv-implies-equal-symbol-name-1
  (implies (symbol-equiv x x-equiv)
           (equal (symbol-name x)
                  (symbol-name x-equiv)))
  :rule-classes (:congruence))