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Newline

Newline-equiv

Basic equivalence relation for newline structures.

Definitions and Theorems

Function: newline-equiv$inline

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

Theorem: newline-equiv-is-an-equivalence

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

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

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

Theorem: newline-fix-under-newline-equiv

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

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

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

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

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

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

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

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

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