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Representation-of-integer-operations

Eq-ullong-ullong

Equality of a value of type unsigned long long and a value of type unsigned long long [C17:6.5.9].

Definitions and Theorems

Function: eq-ullong-ullong

(defun eq-ullong-ullong (x y)
  (declare (xargs :guard (and (ullongp x) (ullongp y))))
  (if (= (integer-from-ullong x)
         (integer-from-ullong y))
      (sint-from-integer 1)
    (sint-from-integer 0)))

Theorem: sintp-of-eq-ullong-ullong

(defthm sintp-of-eq-ullong-ullong
  (sintp (eq-ullong-ullong x y)))

Theorem: eq-ullong-ullong-of-ullong-fix-x

(defthm eq-ullong-ullong-of-ullong-fix-x
  (equal (eq-ullong-ullong (ullong-fix x) y)
         (eq-ullong-ullong x y)))

Theorem: eq-ullong-ullong-ullong-equiv-congruence-on-x

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

Theorem: eq-ullong-ullong-of-ullong-fix-y

(defthm eq-ullong-ullong-of-ullong-fix-y
  (equal (eq-ullong-ullong x (ullong-fix y))
         (eq-ullong-ullong x y)))

Theorem: eq-ullong-ullong-ullong-equiv-congruence-on-y

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