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Representation-of-integer-operations

Eq-ulong-uint

Equality of a value of type unsigned long and a value of type unsigned int [C:6.5.9].

Definitions and Theorems

Function: eq-ulong-uint

(defun eq-ulong-uint (x y)
  (declare (xargs :guard (and (ulongp x) (uintp y))))
  (eq-ulong-ulong x (ulong-from-uint y)))

Theorem: sintp-of-eq-ulong-uint

(defthm sintp-of-eq-ulong-uint
  (sintp (eq-ulong-uint x y)))

Theorem: eq-ulong-uint-of-ulong-fix-x

(defthm eq-ulong-uint-of-ulong-fix-x
  (equal (eq-ulong-uint (ulong-fix x) y)
         (eq-ulong-uint x y)))

Theorem: eq-ulong-uint-ulong-equiv-congruence-on-x

(defthm eq-ulong-uint-ulong-equiv-congruence-on-x
  (implies (ulong-equiv x x-equiv)
           (equal (eq-ulong-uint x y)
                  (eq-ulong-uint x-equiv y)))
  :rule-classes :congruence)

Theorem: eq-ulong-uint-of-uint-fix-y

(defthm eq-ulong-uint-of-uint-fix-y
  (equal (eq-ulong-uint x (uint-fix y))
         (eq-ulong-uint x y)))

Theorem: eq-ulong-uint-uint-equiv-congruence-on-y

(defthm eq-ulong-uint-uint-equiv-congruence-on-y
  (implies (uint-equiv y y-equiv)
           (equal (eq-ulong-uint x y)
                  (eq-ulong-uint x y-equiv)))
  :rule-classes :congruence)