		Search-engine friendly clone of the ACL2 documentation.

Satlink-parser-state

Satlink-parser-state-equiv

Basic equivalence relation for satlink-parser-state structures.

Definitions and Theorems

Function: satlink-parser-state-equiv$inline

(defun satlink-parser-state-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (satlink-parser-state-p acl2::x)
                              (satlink-parser-state-p acl2::y))))
  (equal (satlink-parser-state-fix acl2::x)
         (satlink-parser-state-fix acl2::y)))

Theorem: satlink-parser-state-equiv-is-an-equivalence

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

Theorem: satlink-parser-state-equiv-implies-equal-satlink-parser-state-fix-1

(defthm
 satlink-parser-state-equiv-implies-equal-satlink-parser-state-fix-1
 (implies (satlink-parser-state-equiv acl2::x x-equiv)
          (equal (satlink-parser-state-fix acl2::x)
                 (satlink-parser-state-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: satlink-parser-state-fix-under-satlink-parser-state-equiv

(defthm satlink-parser-state-fix-under-satlink-parser-state-equiv
  (satlink-parser-state-equiv (satlink-parser-state-fix acl2::x)
                              acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-satlink-parser-state-fix-1-forward-to-satlink-parser-state-equiv

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

Theorem: equal-of-satlink-parser-state-fix-2-forward-to-satlink-parser-state-equiv

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

Theorem: satlink-parser-state-equiv-of-satlink-parser-state-fix-1-forward

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

Theorem: satlink-parser-state-equiv-of-satlink-parser-state-fix-2-forward

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