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A4vec-operations

A3vec-fix

Symbolic version of 3vec-fix.

Signature
(a3vec-fix x) → x-fix
Arguments: x — Guard (a4vec-p x).
Returns: x-fix — Type (a4vec-p x-fix).

Definitions and Theorems

Function: a3vec-fix

(defun a3vec-fix (x)
  (declare (xargs :guard (a4vec-p x)))
  (let ((__function__ 'a3vec-fix))
    (declare (ignorable __function__))
    (b* (((when (a4vec-syntactic-3vec-p x))
          (a4vec-fix x))
         ((a4vec x)))
      (a4vec (aig-logior-ss x.upper x.lower)
             (aig-logand-ss x.upper x.lower)))))

Theorem: a4vec-p-of-a3vec-fix

(defthm a4vec-p-of-a3vec-fix
  (b* ((x-fix (a3vec-fix x)))
    (a4vec-p x-fix))
  :rule-classes :rewrite)

Theorem: a3vec-fix-correct

(defthm a3vec-fix-correct
  (equal (a4vec-eval (a3vec-fix x) env)
         (3vec-fix (a4vec-eval x env))))

Theorem: a3vec-fix-of-a4vec-fix-x

(defthm a3vec-fix-of-a4vec-fix-x
  (equal (a3vec-fix (a4vec-fix x))
         (a3vec-fix x)))

Theorem: a3vec-fix-a4vec-equiv-congruence-on-x

(defthm a3vec-fix-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a3vec-fix x)
                  (a3vec-fix x-equiv)))
  :rule-classes :congruence)