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