Basic equivalence relation for svtv-assigns-override-config structures.
Function:
(defun svtv-assigns-override-config-equiv$inline (x y) (declare (xargs :guard (and (svtv-assigns-override-config-p x) (svtv-assigns-override-config-p y)))) (equal (svtv-assigns-override-config-fix x) (svtv-assigns-override-config-fix y)))
Theorem:
(defthm svtv-assigns-override-config-equiv-is-an-equivalence (and (booleanp (svtv-assigns-override-config-equiv x y)) (svtv-assigns-override-config-equiv x x) (implies (svtv-assigns-override-config-equiv x y) (svtv-assigns-override-config-equiv y x)) (implies (and (svtv-assigns-override-config-equiv x y) (svtv-assigns-override-config-equiv y z)) (svtv-assigns-override-config-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm svtv-assigns-override-config-equiv-implies-equal-svtv-assigns-override-config-fix-1 (implies (svtv-assigns-override-config-equiv x x-equiv) (equal (svtv-assigns-override-config-fix x) (svtv-assigns-override-config-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm svtv-assigns-override-config-fix-under-svtv-assigns-override-config-equiv (svtv-assigns-override-config-equiv (svtv-assigns-override-config-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-svtv-assigns-override-config-fix-1-forward-to-svtv-assigns-override-config-equiv (implies (equal (svtv-assigns-override-config-fix x) y) (svtv-assigns-override-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-svtv-assigns-override-config-fix-2-forward-to-svtv-assigns-override-config-equiv (implies (equal x (svtv-assigns-override-config-fix y)) (svtv-assigns-override-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svtv-assigns-override-config-equiv-of-svtv-assigns-override-config-fix-1-forward (implies (svtv-assigns-override-config-equiv (svtv-assigns-override-config-fix x) y) (svtv-assigns-override-config-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svtv-assigns-override-config-equiv-of-svtv-assigns-override-config-fix-2-forward (implies (svtv-assigns-override-config-equiv x (svtv-assigns-override-config-fix y)) (svtv-assigns-override-config-equiv x y)) :rule-classes :forward-chaining)