Less-than-or-equal-to relation of a value of type
Function:
(defun le-ulong-schar (x y) (declare (xargs :guard (and (ulongp x) (scharp y)))) (le-ulong-ulong x (ulong-from-schar y)))
Theorem:
(defthm sintp-of-le-ulong-schar (sintp (le-ulong-schar x y)))
Theorem:
(defthm le-ulong-schar-of-ulong-fix-x (equal (le-ulong-schar (ulong-fix x) y) (le-ulong-schar x y)))
Theorem:
(defthm le-ulong-schar-ulong-equiv-congruence-on-x (implies (ulong-equiv x x-equiv) (equal (le-ulong-schar x y) (le-ulong-schar x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm le-ulong-schar-of-schar-fix-y (equal (le-ulong-schar x (schar-fix y)) (le-ulong-schar x y)))
Theorem:
(defthm le-ulong-schar-schar-equiv-congruence-on-y (implies (schar-equiv y y-equiv) (equal (le-ulong-schar x y) (le-ulong-schar x y-equiv))) :rule-classes :congruence)