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        • Svtv-spec
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• Svtv

Svtv-fix

Fixing function for svtv structures.

Signature

(svtv-fix x) → new-x

Arguments

x — Guard (svtv-p x).

Returns

new-x — Type (svtv-p new-x).

Definitions and Theorems

Function: svtv-fix$inline

(defun svtv-fix$inline (x)
 (declare (xargs :guard (svtv-p x)))
 (let ((__function__ 'svtv-fix))
  (declare (ignorable __function__))
  (mbe :logic
       (b* ((name (acl2::symbol-fix (std::da-nth 0 x)))
            (outexprs (svex-alist-fix (std::da-nth 1 x)))
            (nextstate (svex-alist-fix (std::da-nth 2 x)))
            (states (svex-alistlist-fix (std::da-nth 3 x)))
            (inmasks (svar-boolmasks-fix (std::da-nth 4 x)))
            (outmasks (svar-boolmasks-fix (std::da-nth 5 x)))
            (inmap (svtv-inputmap-fix (std::da-nth 6 x)))
            (orig-ins (true-list-list-fix (std::da-nth 7 x)))
            (orig-overrides (true-list-list-fix (std::da-nth 8 x)))
            (orig-outs (true-list-list-fix (std::da-nth 9 x)))
            (orig-internals (true-list-list-fix (std::da-nth 10 x)))
            (expanded-ins (svtv-lines-fix (std::da-nth 11 x)))
            (expanded-overrides (svtv-lines-fix (std::da-nth 12 x)))
            (nphases (nfix (std::da-nth 13 x)))
            (labels (acl2::symbol-list-fix (std::da-nth 14 x)))
            (form (std::da-nth 15 x)))
         (list name outexprs nextstate states inmasks
               outmasks inmap orig-ins orig-overrides
               orig-outs orig-internals expanded-ins
               expanded-overrides nphases labels form))
       :exec x)))

Theorem: svtv-p-of-svtv-fix

(defthm svtv-p-of-svtv-fix
  (b* ((new-x (svtv-fix$inline x)))
    (svtv-p new-x))
  :rule-classes :rewrite)

Theorem: svtv-fix-when-svtv-p

(defthm svtv-fix-when-svtv-p
  (implies (svtv-p x)
           (equal (svtv-fix x) x)))

Function: svtv-equiv$inline

(defun svtv-equiv$inline (x y)
  (declare (xargs :guard (and (svtv-p x) (svtv-p y))))
  (equal (svtv-fix x) (svtv-fix y)))

Theorem: svtv-equiv-is-an-equivalence

(defthm svtv-equiv-is-an-equivalence
  (and (booleanp (svtv-equiv x y))
       (svtv-equiv x x)
       (implies (svtv-equiv x y)
                (svtv-equiv y x))
       (implies (and (svtv-equiv x y) (svtv-equiv y z))
                (svtv-equiv x z)))
  :rule-classes (:equivalence))

Theorem: svtv-equiv-implies-equal-svtv-fix-1

(defthm svtv-equiv-implies-equal-svtv-fix-1
  (implies (svtv-equiv x x-equiv)
           (equal (svtv-fix x) (svtv-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: svtv-fix-under-svtv-equiv

(defthm svtv-fix-under-svtv-equiv
  (svtv-equiv (svtv-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-svtv-fix-1-forward-to-svtv-equiv

(defthm equal-of-svtv-fix-1-forward-to-svtv-equiv
  (implies (equal (svtv-fix x) y)
           (svtv-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-svtv-fix-2-forward-to-svtv-equiv

(defthm equal-of-svtv-fix-2-forward-to-svtv-equiv
  (implies (equal x (svtv-fix y))
           (svtv-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svtv-equiv-of-svtv-fix-1-forward

(defthm svtv-equiv-of-svtv-fix-1-forward
  (implies (svtv-equiv (svtv-fix x) y)
           (svtv-equiv x y))
  :rule-classes :forward-chaining)

Theorem: svtv-equiv-of-svtv-fix-2-forward

(defthm svtv-equiv-of-svtv-fix-2-forward
  (implies (svtv-equiv x (svtv-fix y))
           (svtv-equiv x y))
  :rule-classes :forward-chaining)