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Console-result

Console-result-equiv

Basic equivalence relation for console-result structures.

Definitions and Theorems

Function: console-result-equiv$inline

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

Theorem: console-result-equiv-is-an-equivalence

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

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

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

Theorem: console-result-fix-under-console-result-equiv

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

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

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

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

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

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

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

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

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