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Representation-of-integer-operations

Shl-ullong-sint-okp

Check if the left shift of a value of type unsigned long long by a value of type signed int is well-defined.

Definitions and Theorems

Function: shl-ullong-sint-okp

(defun shl-ullong-sint-okp (x y)
  (declare (xargs :guard (and (ullongp x) (sintp y))))
  (shl-ullong-okp x (integer-from-sint y)))

Theorem: booleanp-of-shl-ullong-sint-okp

(defthm booleanp-of-shl-ullong-sint-okp
  (booleanp (shl-ullong-sint-okp x y)))

Theorem: shl-ullong-sint-okp-of-ullong-fix-x

(defthm shl-ullong-sint-okp-of-ullong-fix-x
  (equal (shl-ullong-sint-okp (ullong-fix x) y)
         (shl-ullong-sint-okp x y)))

Theorem: shl-ullong-sint-okp-ullong-equiv-congruence-on-x

(defthm shl-ullong-sint-okp-ullong-equiv-congruence-on-x
  (implies (ullong-equiv x x-equiv)
           (equal (shl-ullong-sint-okp x y)
                  (shl-ullong-sint-okp x-equiv y)))
  :rule-classes :congruence)

Theorem: shl-ullong-sint-okp-of-sint-fix-y

(defthm shl-ullong-sint-okp-of-sint-fix-y
  (equal (shl-ullong-sint-okp x (sint-fix y))
         (shl-ullong-sint-okp x y)))

Theorem: shl-ullong-sint-okp-sint-equiv-congruence-on-y

(defthm shl-ullong-sint-okp-sint-equiv-congruence-on-y
  (implies (sint-equiv y y-equiv)
           (equal (shl-ullong-sint-okp x y)
                  (shl-ullong-sint-okp x y-equiv)))
  :rule-classes :congruence)