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Multiplication of a value of type
Function:
(defun mul-sint-schar (x y) (declare (xargs :guard (and (sintp x) (scharp y) (mul-sint-schar-okp x y)))) (mul-sint-sint x (sint-from-schar y)))
Theorem:
(defthm sintp-of-mul-sint-schar (sintp (mul-sint-schar x y)))
Theorem:
(defthm mul-sint-schar-of-sint-fix-x (equal (mul-sint-schar (sint-fix x) y) (mul-sint-schar x y)))
Theorem:
(defthm mul-sint-schar-sint-equiv-congruence-on-x (implies (sint-equiv x x-equiv) (equal (mul-sint-schar x y) (mul-sint-schar x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm mul-sint-schar-of-schar-fix-y (equal (mul-sint-schar x (schar-fix y)) (mul-sint-schar x y)))
Theorem:
(defthm mul-sint-schar-schar-equiv-congruence-on-y (implies (schar-equiv y y-equiv) (equal (mul-sint-schar x y) (mul-sint-schar x y-equiv))) :rule-classes :congruence)