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Undocumented

Fgl-ev-equiv

This is a universal equivalence, introduced using ACL2::def-universal-equiv.

Function: fgl-ev-equiv

(defun fgl-ev-equiv (x y)
  (declare (xargs :non-executable t))
  (declare (xargs :guard t))
  (prog2$ (acl2::throw-nonexec-error 'fgl-ev-equiv
                                     (list x y))
          (let ((env (fgl-ev-equiv-witness x y)))
            (and (equal (fgl-ev x env)
                        (fgl-ev y env))))))

Definitions and Theorems

Theorem: fgl-ev-equiv-necc

(defthm fgl-ev-equiv-necc
  (implies (not (and (equal (fgl-ev x env) (fgl-ev y env))))
           (not (fgl-ev-equiv x y))))

Theorem: fgl-ev-equiv-is-an-equivalence

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