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Vcd-wirelist

Vcd-wirelist-equiv

Basic equivalence relation for vcd-wirelist structures.

Definitions and Theorems

Function: vcd-wirelist-equiv$inline

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

Theorem: vcd-wirelist-equiv-is-an-equivalence

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

Theorem: vcd-wirelist-equiv-implies-equal-vcd-wirelist-fix-1

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

Theorem: vcd-wirelist-fix-under-vcd-wirelist-equiv

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

Theorem: equal-of-vcd-wirelist-fix-1-forward-to-vcd-wirelist-equiv

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

Theorem: equal-of-vcd-wirelist-fix-2-forward-to-vcd-wirelist-equiv

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

Theorem: vcd-wirelist-equiv-of-vcd-wirelist-fix-1-forward

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

Theorem: vcd-wirelist-equiv-of-vcd-wirelist-fix-2-forward

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