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• Svstmt-config

Svstmt-config-equiv

Basic equivalence relation for svstmt-config structures.

Definitions and Theorems

Function: svstmt-config-equiv$inline

(defun svstmt-config-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (svstmt-config-p acl2::x)
                              (svstmt-config-p acl2::y))))
  (equal (svstmt-config-fix acl2::x)
         (svstmt-config-fix acl2::y)))

Theorem: svstmt-config-equiv-is-an-equivalence

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

Theorem: svstmt-config-equiv-implies-equal-svstmt-config-fix-1

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

Theorem: svstmt-config-fix-under-svstmt-config-equiv

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

Theorem: equal-of-svstmt-config-fix-1-forward-to-svstmt-config-equiv

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

Theorem: equal-of-svstmt-config-fix-2-forward-to-svstmt-config-equiv

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

Theorem: svstmt-config-equiv-of-svstmt-config-fix-1-forward

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

Theorem: svstmt-config-equiv-of-svstmt-config-fix-2-forward

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