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• Constraint-rule

Constraint-rule-fix

Fixing function for constraint-rule structures.

Signature

(constraint-rule-fix x) → new-x

Arguments

x — Guard (constraint-rule-p x).

Returns

new-x — Type (constraint-rule-p new-x).

Definitions and Theorems

Function: constraint-rule-fix$inline

(defun constraint-rule-fix$inline (x)
  (declare (xargs :guard (constraint-rule-p x)))
  (let ((__function__ 'constraint-rule-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((thmname (acl2::symbol-fix (car x)))
              (lit-alist (pseudo-term-subst-fix (car (cdr x))))
              (syntaxp (pseudo-term-fix (cdr (cdr x)))))
           (cons thmname (cons lit-alist syntaxp)))
         :exec x)))

Theorem: constraint-rule-p-of-constraint-rule-fix

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

Theorem: constraint-rule-fix-when-constraint-rule-p

(defthm constraint-rule-fix-when-constraint-rule-p
  (implies (constraint-rule-p x)
           (equal (constraint-rule-fix x) x)))

Function: constraint-rule-equiv$inline

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

Theorem: constraint-rule-equiv-is-an-equivalence

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

Theorem: constraint-rule-equiv-implies-equal-constraint-rule-fix-1

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

Theorem: constraint-rule-fix-under-constraint-rule-equiv

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

Theorem: equal-of-constraint-rule-fix-1-forward-to-constraint-rule-equiv

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

Theorem: equal-of-constraint-rule-fix-2-forward-to-constraint-rule-equiv

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

Theorem: constraint-rule-equiv-of-constraint-rule-fix-1-forward

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

Theorem: constraint-rule-equiv-of-constraint-rule-fix-2-forward

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