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• Eoutcome

Eoutcome-equiv

Basic equivalence relation for eoutcome structures.

Definitions and Theorems

Function: eoutcome-equiv$inline

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

Theorem: eoutcome-equiv-is-an-equivalence

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

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

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

Theorem: eoutcome-fix-under-eoutcome-equiv

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

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

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

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

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

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

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

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

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