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• Svtv-spec

Svtv-spec-fix

Fixing function for svtv-spec structures.

Signature

(svtv-spec-fix x) → new-x

Arguments

x — Guard (svtv-spec-p x).

Returns

new-x — Type (svtv-spec-p new-x).

Definitions and Theorems

Function: svtv-spec-fix$inline

(defun svtv-spec-fix$inline (x)
 (declare (xargs :guard (svtv-spec-p x)))
 (let ((__function__ 'svtv-spec-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (b* ((fsm (fsm-fix (cdr (std::da-nth 0 x))))
           (cycle-phases
                (svtv-cyclephaselist-fix (cdr (std::da-nth 1 x))))
           (namemap (svtv-name-lhs-map-fix (cdr (std::da-nth 2 x))))
           (probes (svtv-probealist-fix (cdr (std::da-nth 3 x))))
           (in-alists (svex-alistlist-fix (cdr (std::da-nth 4 x))))
           (override-test-alists
                (svex-alistlist-fix (cdr (std::da-nth 5 x))))
           (override-val-alists
                (svex-alistlist-fix (cdr (std::da-nth 6 x))))
           (initst-alist (svex-alist-fix (cdr (std::da-nth 7 x)))))
        (list (cons 'fsm fsm)
              (cons 'cycle-phases cycle-phases)
              (cons 'namemap namemap)
              (cons 'probes probes)
              (cons 'in-alists in-alists)
              (cons 'override-test-alists
                    override-test-alists)
              (cons 'override-val-alists
                    override-val-alists)
              (cons 'initst-alist initst-alist)))
      :exec x)))

Theorem: svtv-spec-p-of-svtv-spec-fix

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

Theorem: svtv-spec-fix-when-svtv-spec-p

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

Function: svtv-spec-equiv$inline

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

Theorem: svtv-spec-equiv-is-an-equivalence

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

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

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

Theorem: svtv-spec-fix-under-svtv-spec-equiv

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

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

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

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

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

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

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

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

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