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Representation-of-integer-operations

Shl-schar

Left shift of a value of type signed char by an integer [C:6.5.7].

Definitions and Theorems

Function: shl-schar

(defun shl-schar (x y)
  (declare (xargs :guard (and (scharp x)
                              (integerp y)
                              (shl-schar-okp x y))))
  (shl-sint (sint-from-schar x) y))

Theorem: sintp-of-shl-schar

(defthm sintp-of-shl-schar
  (sintp (shl-schar x y)))

Theorem: shl-schar-of-schar-fix-x

(defthm shl-schar-of-schar-fix-x
  (equal (shl-schar (schar-fix x) y)
         (shl-schar x y)))

Theorem: shl-schar-schar-equiv-congruence-on-x

(defthm shl-schar-schar-equiv-congruence-on-x
  (implies (schar-equiv x x-equiv)
           (equal (shl-schar x y)
                  (shl-schar x-equiv y)))
  :rule-classes :congruence)

Theorem: shl-schar-of-ifix-y

(defthm shl-schar-of-ifix-y
  (equal (shl-schar x (ifix y))
         (shl-schar x y)))

Theorem: shl-schar-int-equiv-congruence-on-y

(defthm shl-schar-int-equiv-congruence-on-y
  (implies (acl2::int-equiv y y-equiv)
           (equal (shl-schar x y)
                  (shl-schar x y-equiv)))
  :rule-classes :congruence)