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• Obligation-hyp

Obligation-hyp-equiv

Basic equivalence relation for obligation-hyp structures.

Definitions and Theorems

Function: obligation-hyp-equiv$inline

(defun obligation-hyp-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (obligation-hypp acl2::x)
                              (obligation-hypp acl2::y))))
  (equal (obligation-hyp-fix acl2::x)
         (obligation-hyp-fix acl2::y)))

Theorem: obligation-hyp-equiv-is-an-equivalence

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

Theorem: obligation-hyp-equiv-implies-equal-obligation-hyp-fix-1

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

Theorem: obligation-hyp-fix-under-obligation-hyp-equiv

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

Theorem: equal-of-obligation-hyp-fix-1-forward-to-obligation-hyp-equiv

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

Theorem: equal-of-obligation-hyp-fix-2-forward-to-obligation-hyp-equiv

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

Theorem: obligation-hyp-equiv-of-obligation-hyp-fix-1-forward

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

Theorem: obligation-hyp-equiv-of-obligation-hyp-fix-2-forward

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