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Structdeclor

Structdeclor-equiv

Basic equivalence relation for structdeclor structures.

Definitions and Theorems

Function: structdeclor-equiv$inline

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

Theorem: structdeclor-equiv-is-an-equivalence

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

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

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

Theorem: structdeclor-fix-under-structdeclor-equiv

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

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

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

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

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

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

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

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

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