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Constraint-instance

Constraint-instance-equiv

Basic equivalence relation for constraint-instance structures.

Definitions and Theorems

Function: constraint-instance-equiv$inline

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

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

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

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

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

Theorem: constraint-instance-fix-under-constraint-instance-equiv

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

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

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

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

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

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

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

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

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