		Search-engine friendly clone of the ACL2 documentation.

S4vecs

S4vec-override

Signature
(s4vec-override strong weak) → res
Arguments: strong — Guard (s4vec-p strong).; weak — Guard (s4vec-p weak).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-override

(defun s4vec-override (strong weak)
 (declare (xargs :guard (and (s4vec-p strong) (s4vec-p weak))))
 (let ((__function__ 's4vec-override))
  (declare (ignorable __function__))
  (b* (((s4vec strong)) ((s4vec weak)))
    (s4vec
         (sparseint-bitor (sparseint-bitand strong.lower weak.upper)
                          strong.upper)
         (sparseint-bitand (sparseint-bitor strong.upper weak.lower)
                           strong.lower)))))

Theorem: s4vec-p-of-s4vec-override

(defthm s4vec-p-of-s4vec-override
  (b* ((res (s4vec-override strong weak)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-override-correct

(defthm s4vec-override-correct
  (b* ((?res (s4vec-override strong weak)))
    (equal (s4vec->4vec res)
           (4vec-override (s4vec->4vec strong)
                          (s4vec->4vec weak)))))

Theorem: s4vec-override-of-s4vec-fix-strong

(defthm s4vec-override-of-s4vec-fix-strong
  (equal (s4vec-override (s4vec-fix strong) weak)
         (s4vec-override strong weak)))

Theorem: s4vec-override-s4vec-equiv-congruence-on-strong

(defthm s4vec-override-s4vec-equiv-congruence-on-strong
  (implies (s4vec-equiv strong strong-equiv)
           (equal (s4vec-override strong weak)
                  (s4vec-override strong-equiv weak)))
  :rule-classes :congruence)

Theorem: s4vec-override-of-s4vec-fix-weak

(defthm s4vec-override-of-s4vec-fix-weak
  (equal (s4vec-override strong (s4vec-fix weak))
         (s4vec-override strong weak)))

Theorem: s4vec-override-s4vec-equiv-congruence-on-weak

(defthm s4vec-override-s4vec-equiv-congruence-on-weak
  (implies (s4vec-equiv weak weak-equiv)
           (equal (s4vec-override strong weak)
                  (s4vec-override strong weak-equiv)))
  :rule-classes :congruence)