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• Lhprobe-constraint

Lhprobe-constraint-equiv

Basic equivalence relation for lhprobe-constraint structures.

Definitions and Theorems

Function: lhprobe-constraint-equiv$inline

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

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

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

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

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

Theorem: lhprobe-constraint-fix-under-lhprobe-constraint-equiv

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

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

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

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

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

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

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

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

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