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