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• Fgl-config

Fgl-config-equiv

Basic equivalence relation for fgl-config structures.

Definitions and Theorems

Function: fgl-config-equiv$inline

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

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

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

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

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

Theorem: fgl-config-fix-under-fgl-config-equiv

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

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

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

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

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

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

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

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

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