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Pseudo-event-form

Fixtype of pseudo event forms.

The recognizer is pseudo-event-formp and the fixer is pseudo-event-form-fix.

Definitions and Theorems

Function: pseudo-event-form-equiv$inline

(defun pseudo-event-form-equiv$inline (x y)
       (declare (xargs :guard (and (pseudo-event-formp x)
                                   (pseudo-event-formp y))))
       (equal (pseudo-event-form-fix x)
              (pseudo-event-form-fix y)))

Theorem: pseudo-event-form-equiv-is-an-equivalence

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

Theorem: pseudo-event-form-equiv-implies-equal-pseudo-event-form-fix-1

(defthm
     pseudo-event-form-equiv-implies-equal-pseudo-event-form-fix-1
     (implies (pseudo-event-form-equiv x x-equiv)
              (equal (pseudo-event-form-fix x)
                     (pseudo-event-form-fix x-equiv)))
     :rule-classes (:congruence))

Theorem: pseudo-event-form-fix-under-pseudo-event-form-equiv

(defthm pseudo-event-form-fix-under-pseudo-event-form-equiv
        (pseudo-event-form-equiv (pseudo-event-form-fix x)
                                 x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-pseudo-event-form-fix-1-forward-to-pseudo-event-form-equiv

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

Theorem: equal-of-pseudo-event-form-fix-2-forward-to-pseudo-event-form-equiv

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

Theorem: pseudo-event-form-equiv-of-pseudo-event-form-fix-1-forward

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

Theorem: pseudo-event-form-equiv-of-pseudo-event-form-fix-2-forward

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