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• Svex-apply
• 4vec-<<=

Svex-apply-monotonocity

svex-apply is almost always monotonic :-(

Definitions and Theorems

Theorem: svex-apply-monotonic

(defthm svex-apply-monotonic
  (implies (and (4veclist-<<= x y)
                (not (eq (fnsym-fix fn) '===))
                (or (not (eq (fnsym-fix fn) '===*))
                    (equal (4veclist-nth-safe 1 x)
                           (4veclist-nth-safe 1 y)))
                (or (not (eq (fnsym-fix fn) '==?))
                    (equal (4veclist-nth-safe 1 x)
                           (4veclist-nth-safe 1 y)))
                (or (not (eq (fnsym-fix fn) 'bit?!))
                    (equal (4veclist-nth-safe 0 x)
                           (4veclist-nth-safe 0 y)))
                (or (not (eq (fnsym-fix fn) '?!))
                    (equal (4veclist-nth-safe 0 x)
                           (4veclist-nth-safe 0 y))))
           (4vec-<<= (svex-apply fn x)
                     (svex-apply fn y))))