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• Defdefparse-function-spec

Defdefparse-function-spec-equiv

Basic equivalence relation for defdefparse-function-spec structures.

Definitions and Theorems

Function: defdefparse-function-spec-equiv$inline

(defun defdefparse-function-spec-equiv$inline (acl2::x acl2::y)
  (declare
       (xargs :guard (and (defdefparse-function-spec-p acl2::x)
                          (defdefparse-function-spec-p acl2::y))))
  (equal (defdefparse-function-spec-fix acl2::x)
         (defdefparse-function-spec-fix acl2::y)))

Theorem: defdefparse-function-spec-equiv-is-an-equivalence

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

Theorem: defdefparse-function-spec-equiv-implies-equal-defdefparse-function-spec-fix-1

(defthm
 defdefparse-function-spec-equiv-implies-equal-defdefparse-function-spec-fix-1
 (implies (defdefparse-function-spec-equiv acl2::x x-equiv)
          (equal (defdefparse-function-spec-fix acl2::x)
                 (defdefparse-function-spec-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: defdefparse-function-spec-fix-under-defdefparse-function-spec-equiv

(defthm
 defdefparse-function-spec-fix-under-defdefparse-function-spec-equiv
 (defdefparse-function-spec-equiv
      (defdefparse-function-spec-fix acl2::x)
      acl2::x)
 :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-defdefparse-function-spec-fix-1-forward-to-defdefparse-function-spec-equiv

(defthm
 equal-of-defdefparse-function-spec-fix-1-forward-to-defdefparse-function-spec-equiv
 (implies (equal (defdefparse-function-spec-fix acl2::x)
                 acl2::y)
          (defdefparse-function-spec-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-defdefparse-function-spec-fix-2-forward-to-defdefparse-function-spec-equiv

(defthm
 equal-of-defdefparse-function-spec-fix-2-forward-to-defdefparse-function-spec-equiv
 (implies (equal acl2::x
                 (defdefparse-function-spec-fix acl2::y))
          (defdefparse-function-spec-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: defdefparse-function-spec-equiv-of-defdefparse-function-spec-fix-1-forward

(defthm
 defdefparse-function-spec-equiv-of-defdefparse-function-spec-fix-1-forward
 (implies (defdefparse-function-spec-equiv
               (defdefparse-function-spec-fix acl2::x)
               acl2::y)
          (defdefparse-function-spec-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: defdefparse-function-spec-equiv-of-defdefparse-function-spec-fix-2-forward

(defthm
 defdefparse-function-spec-equiv-of-defdefparse-function-spec-fix-2-forward
 (implies (defdefparse-function-spec-equiv
               acl2::x
               (defdefparse-function-spec-fix acl2::y))
          (defdefparse-function-spec-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)