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Console

Console-equiv

Basic equivalence relation for console structures.

Definitions and Theorems

Function: console-equiv$inline

(defun console-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (consolep acl2::x)
                              (consolep acl2::y))))
  (equal (console-fix acl2::x)
         (console-fix acl2::y)))

Theorem: console-equiv-is-an-equivalence

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

Theorem: console-equiv-implies-equal-console-fix-1

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

Theorem: console-fix-under-console-equiv

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

Theorem: equal-of-console-fix-1-forward-to-console-equiv

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

Theorem: equal-of-console-fix-2-forward-to-console-equiv

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

Theorem: console-equiv-of-console-fix-1-forward

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

Theorem: console-equiv-of-console-fix-2-forward

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