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• Screen-message

Screen-message-equiv

Basic equivalence relation for screen-message structures.

Definitions and Theorems

Function: screen-message-equiv$inline

(defun screen-message-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (screen-messagep acl2::x)
                              (screen-messagep acl2::y))))
  (equal (screen-message-fix acl2::x)
         (screen-message-fix acl2::y)))

Theorem: screen-message-equiv-is-an-equivalence

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

Theorem: screen-message-equiv-implies-equal-screen-message-fix-1

(defthm screen-message-equiv-implies-equal-screen-message-fix-1
  (implies (screen-message-equiv acl2::x x-equiv)
           (equal (screen-message-fix acl2::x)
                  (screen-message-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: screen-message-fix-under-screen-message-equiv

(defthm screen-message-fix-under-screen-message-equiv
  (screen-message-equiv (screen-message-fix acl2::x)
                        acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-screen-message-fix-1-forward-to-screen-message-equiv

(defthm
      equal-of-screen-message-fix-1-forward-to-screen-message-equiv
  (implies (equal (screen-message-fix acl2::x)
                  acl2::y)
           (screen-message-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-screen-message-fix-2-forward-to-screen-message-equiv

(defthm
      equal-of-screen-message-fix-2-forward-to-screen-message-equiv
  (implies (equal acl2::x (screen-message-fix acl2::y))
           (screen-message-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: screen-message-equiv-of-screen-message-fix-1-forward

(defthm screen-message-equiv-of-screen-message-fix-1-forward
  (implies (screen-message-equiv (screen-message-fix acl2::x)
                                 acl2::y)
           (screen-message-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: screen-message-equiv-of-screen-message-fix-2-forward

(defthm screen-message-equiv-of-screen-message-fix-2-forward
  (implies
       (screen-message-equiv acl2::x (screen-message-fix acl2::y))
       (screen-message-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)