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Representation-of-integer-operations

Eq-sshort-sshort

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

Definitions and Theorems

Function: eq-sshort-sshort

(defun eq-sshort-sshort (x y)
  (declare (xargs :guard (and (sshortp x) (sshortp y))))
  (eq-sint-sint (sint-from-sshort x)
                (sint-from-sshort y)))

Theorem: sintp-of-eq-sshort-sshort

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

Theorem: eq-sshort-sshort-of-sshort-fix-x

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

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

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

Theorem: eq-sshort-sshort-of-sshort-fix-y

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

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

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