		Search-engine friendly clone of the ACL2 documentation.

Phase-fsm-config

Phase-fsm-config-equiv

Basic equivalence relation for phase-fsm-config structures.

Definitions and Theorems

Function: phase-fsm-config-equiv$inline

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

Theorem: phase-fsm-config-equiv-is-an-equivalence

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

Theorem: phase-fsm-config-equiv-implies-equal-phase-fsm-config-fix-1

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

Theorem: phase-fsm-config-fix-under-phase-fsm-config-equiv

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

Theorem: equal-of-phase-fsm-config-fix-1-forward-to-phase-fsm-config-equiv

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

Theorem: equal-of-phase-fsm-config-fix-2-forward-to-phase-fsm-config-equiv

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

Theorem: phase-fsm-config-equiv-of-phase-fsm-config-fix-1-forward

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

Theorem: phase-fsm-config-equiv-of-phase-fsm-config-fix-2-forward

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