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Representation-of-integer-operations

Eq-sllong-sllong

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

Definitions and Theorems

Function: eq-sllong-sllong

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

Theorem: sintp-of-eq-sllong-sllong

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

Theorem: eq-sllong-sllong-of-sllong-fix-x

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

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

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

Theorem: eq-sllong-sllong-of-sllong-fix-y

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

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

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