Equality of a value of type
Function:
(defun eq-uint-uint (x y) (declare (xargs :guard (and (uintp x) (uintp y)))) (if (= (integer-from-uint x) (integer-from-uint y)) (sint-from-integer 1) (sint-from-integer 0)))
Theorem:
(defthm sintp-of-eq-uint-uint (sintp (eq-uint-uint x y)))
Theorem:
(defthm eq-uint-uint-of-uint-fix-x (equal (eq-uint-uint (uint-fix x) y) (eq-uint-uint x y)))
Theorem:
(defthm eq-uint-uint-uint-equiv-congruence-on-x (implies (uint-equiv x x-equiv) (equal (eq-uint-uint x y) (eq-uint-uint x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm eq-uint-uint-of-uint-fix-y (equal (eq-uint-uint x (uint-fix y)) (eq-uint-uint x y)))
Theorem:
(defthm eq-uint-uint-uint-equiv-congruence-on-y (implies (uint-equiv y y-equiv) (equal (eq-uint-uint x y) (eq-uint-uint x y-equiv))) :rule-classes :congruence)