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• Parametrize-config

Parametrize-config-equiv

Basic equivalence relation for parametrize-config structures.

Definitions and Theorems

Function: parametrize-config-equiv$inline

(defun parametrize-config-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (parametrize-config-p x)
                              (parametrize-config-p acl2::y))))
  (equal (parametrize-config-fix x)
         (parametrize-config-fix acl2::y)))

Theorem: parametrize-config-equiv-is-an-equivalence

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

Theorem: parametrize-config-equiv-implies-equal-parametrize-config-fix-1

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

Theorem: parametrize-config-fix-under-parametrize-config-equiv

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

Theorem: equal-of-parametrize-config-fix-1-forward-to-parametrize-config-equiv

(defthm
 equal-of-parametrize-config-fix-1-forward-to-parametrize-config-equiv
 (implies (equal (parametrize-config-fix x)
                 acl2::y)
          (parametrize-config-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-parametrize-config-fix-2-forward-to-parametrize-config-equiv

(defthm
 equal-of-parametrize-config-fix-2-forward-to-parametrize-config-equiv
 (implies (equal x (parametrize-config-fix acl2::y))
          (parametrize-config-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: parametrize-config-equiv-of-parametrize-config-fix-1-forward

(defthm parametrize-config-equiv-of-parametrize-config-fix-1-forward
  (implies (parametrize-config-equiv (parametrize-config-fix x)
                                     acl2::y)
           (parametrize-config-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: parametrize-config-equiv-of-parametrize-config-fix-2-forward

(defthm parametrize-config-equiv-of-parametrize-config-fix-2-forward
  (implies
       (parametrize-config-equiv x (parametrize-config-fix acl2::y))
       (parametrize-config-equiv x acl2::y))
  :rule-classes :forward-chaining)