Basic equivalence relation for partys/declor/ambig structures.
Function:
(defun partys/declor/ambig-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (partys/declor/ambig-p acl2::x) (partys/declor/ambig-p acl2::y)))) (equal (partys/declor/ambig-fix acl2::x) (partys/declor/ambig-fix acl2::y)))
Theorem:
(defthm partys/declor/ambig-equiv-is-an-equivalence (and (booleanp (partys/declor/ambig-equiv x y)) (partys/declor/ambig-equiv x x) (implies (partys/declor/ambig-equiv x y) (partys/declor/ambig-equiv y x)) (implies (and (partys/declor/ambig-equiv x y) (partys/declor/ambig-equiv y z)) (partys/declor/ambig-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm partys/declor/ambig-equiv-implies-equal-partys/declor/ambig-fix-1 (implies (partys/declor/ambig-equiv acl2::x x-equiv) (equal (partys/declor/ambig-fix acl2::x) (partys/declor/ambig-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm partys/declor/ambig-fix-under-partys/declor/ambig-equiv (partys/declor/ambig-equiv (partys/declor/ambig-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-partys/declor/ambig-fix-1-forward-to-partys/declor/ambig-equiv (implies (equal (partys/declor/ambig-fix acl2::x) acl2::y) (partys/declor/ambig-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-partys/declor/ambig-fix-2-forward-to-partys/declor/ambig-equiv (implies (equal acl2::x (partys/declor/ambig-fix acl2::y)) (partys/declor/ambig-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm partys/declor/ambig-equiv-of-partys/declor/ambig-fix-1-forward (implies (partys/declor/ambig-equiv (partys/declor/ambig-fix acl2::x) acl2::y) (partys/declor/ambig-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm partys/declor/ambig-equiv-of-partys/declor/ambig-fix-2-forward (implies (partys/declor/ambig-equiv acl2::x (partys/declor/ambig-fix acl2::y)) (partys/declor/ambig-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)