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