Equality of a value of type
Function:
(defun eq-sint-ullong (x y) (declare (xargs :guard (and (sintp x) (ullongp y)))) (eq-ullong-ullong (ullong-from-sint x) y))
Theorem:
(defthm sintp-of-eq-sint-ullong (sintp (eq-sint-ullong x y)))
Theorem:
(defthm eq-sint-ullong-of-sint-fix-x (equal (eq-sint-ullong (sint-fix x) y) (eq-sint-ullong x y)))
Theorem:
(defthm eq-sint-ullong-sint-equiv-congruence-on-x (implies (sint-equiv x x-equiv) (equal (eq-sint-ullong x y) (eq-sint-ullong x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm eq-sint-ullong-of-ullong-fix-y (equal (eq-sint-ullong x (ullong-fix y)) (eq-sint-ullong x y)))
Theorem:
(defthm eq-sint-ullong-ullong-equiv-congruence-on-y (implies (ullong-equiv y y-equiv) (equal (eq-sint-ullong x y) (eq-sint-ullong x y-equiv))) :rule-classes :congruence)