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