Left shift of a value of type
Function:
(defun shl-sshort-sint (x y) (declare (xargs :guard (and (sshortp x) (sintp y) (shl-sshort-sint-okp x y)))) (shl-sshort x (integer-from-sint y)))
Theorem:
(defthm sintp-of-shl-sshort-sint (sintp (shl-sshort-sint x y)))
Theorem:
(defthm shl-sshort-sint-of-sshort-fix-x (equal (shl-sshort-sint (sshort-fix x) y) (shl-sshort-sint x y)))
Theorem:
(defthm shl-sshort-sint-sshort-equiv-congruence-on-x (implies (sshort-equiv x x-equiv) (equal (shl-sshort-sint x y) (shl-sshort-sint x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm shl-sshort-sint-of-sint-fix-y (equal (shl-sshort-sint x (sint-fix y)) (shl-sshort-sint x y)))
Theorem:
(defthm shl-sshort-sint-sint-equiv-congruence-on-y (implies (sint-equiv y y-equiv) (equal (shl-sshort-sint x y) (shl-sshort-sint x y-equiv))) :rule-classes :congruence)