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Maybe-a3vec-fix

Signature

(maybe-a3vec-fix v x) → vv

Arguments

v — Guard (a4vec-p v).

x — Guard (svex-p x).

Returns

vv — Type (a4vec-p vv).

Definitions and Theorems

Function: maybe-a3vec-fix

(defun maybe-a3vec-fix (v x)
  (declare (xargs :guard (and (a4vec-p v) (svex-p x))))
  (let ((__function__ 'maybe-a3vec-fix))
    (declare (ignorable __function__))
    (if (3valued-syntaxp (svex-fix x))
        (a4vec-fix v)
      (a3vec-fix v))))

Theorem: a4vec-p-of-maybe-a3vec-fix

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

Theorem: maybe-a3vec-fix-when-implies

(defthm maybe-a3vec-fix-when-implies
  (implies (case-split (implies (3valued-syntaxp x)
                                (3vec-p (a4vec-eval v env))))
           (equal (a4vec-eval (maybe-a3vec-fix v x) env)
                  (3vec-fix (a4vec-eval v env)))))

Theorem: maybe-a3vec-fix-of-nths

(defthm maybe-a3vec-fix-of-nths
  (implies
       (equal (a4veclist-eval vals env)
              (svexlist-eval x (svex-a4vec-env-eval a4env env)))
       (equal (a4vec-eval (maybe-a3vec-fix (nth n vals) (nth n x))
                          env)
              (3vec-fix (a4vec-eval (nth n vals) env)))))

Theorem: maybe-a3vec-fix-of-a3vec

(defthm maybe-a3vec-fix-of-a3vec
  (implies (a4vec-syntactic-3vec-p v)
           (equal (maybe-a3vec-fix v x)
                  (a4vec-fix v))))

Theorem: maybe-a3vec-fix-of-a4vec-fix-v

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

Theorem: maybe-a3vec-fix-a4vec-equiv-congruence-on-v

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

Theorem: maybe-a3vec-fix-of-svex-fix-x

(defthm maybe-a3vec-fix-of-svex-fix-x
  (equal (maybe-a3vec-fix v (svex-fix x))
         (maybe-a3vec-fix v x)))

Theorem: maybe-a3vec-fix-svex-equiv-congruence-on-x

(defthm maybe-a3vec-fix-svex-equiv-congruence-on-x
  (implies (svex-equiv x x-equiv)
           (equal (maybe-a3vec-fix v x)
                  (maybe-a3vec-fix v x-equiv)))
  :rule-classes :congruence)