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• Char+short+int+long+llong+bool-format

Char+short+int+long+llong+bool-format-equiv

Basic equivalence relation for char+short+int+long+llong+bool-format structures.

Definitions and Theorems

Function: char+short+int+long+llong+bool-format-equiv$inline

(defun char+short+int+long+llong+bool-format-equiv$inline
       (acl2::x acl2::y)
 (declare
  (xargs
     :guard (and (char+short+int+long+llong+bool-formatp acl2::x)
                 (char+short+int+long+llong+bool-formatp acl2::y))))
 (equal (char+short+int+long+llong+bool-format-fix acl2::x)
        (char+short+int+long+llong+bool-format-fix acl2::y)))

Theorem: char+short+int+long+llong+bool-format-equiv-is-an-equivalence

(defthm
      char+short+int+long+llong+bool-format-equiv-is-an-equivalence
 (and
    (booleanp (char+short+int+long+llong+bool-format-equiv x y))
    (char+short+int+long+llong+bool-format-equiv x x)
    (implies (char+short+int+long+llong+bool-format-equiv x y)
             (char+short+int+long+llong+bool-format-equiv y x))
    (implies (and (char+short+int+long+llong+bool-format-equiv x y)
                  (char+short+int+long+llong+bool-format-equiv y z))
             (char+short+int+long+llong+bool-format-equiv x z)))
 :rule-classes (:equivalence))

Theorem: char+short+int+long+llong+bool-format-equiv-implies-equal-char+short+int+long+llong+bool-format-fix-1

(defthm
 char+short+int+long+llong+bool-format-equiv-implies-equal-char+short+int+long+llong+bool-format-fix-1
 (implies
      (char+short+int+long+llong+bool-format-equiv acl2::x x-equiv)
      (equal (char+short+int+long+llong+bool-format-fix acl2::x)
             (char+short+int+long+llong+bool-format-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: char+short+int+long+llong+bool-format-fix-under-char+short+int+long+llong+bool-format-equiv

(defthm
 char+short+int+long+llong+bool-format-fix-under-char+short+int+long+llong+bool-format-equiv
 (char+short+int+long+llong+bool-format-equiv
      (char+short+int+long+llong+bool-format-fix acl2::x)
      acl2::x)
 :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-char+short+int+long+llong+bool-format-fix-1-forward-to-char+short+int+long+llong+bool-format-equiv

(defthm
 equal-of-char+short+int+long+llong+bool-format-fix-1-forward-to-char+short+int+long+llong+bool-format-equiv
 (implies
      (equal (char+short+int+long+llong+bool-format-fix acl2::x)
             acl2::y)
      (char+short+int+long+llong+bool-format-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-char+short+int+long+llong+bool-format-fix-2-forward-to-char+short+int+long+llong+bool-format-equiv

(defthm
 equal-of-char+short+int+long+llong+bool-format-fix-2-forward-to-char+short+int+long+llong+bool-format-equiv
 (implies
      (equal acl2::x
             (char+short+int+long+llong+bool-format-fix acl2::y))
      (char+short+int+long+llong+bool-format-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: char+short+int+long+llong+bool-format-equiv-of-char+short+int+long+llong+bool-format-fix-1-forward

(defthm
 char+short+int+long+llong+bool-format-equiv-of-char+short+int+long+llong+bool-format-fix-1-forward
 (implies
      (char+short+int+long+llong+bool-format-equiv
           (char+short+int+long+llong+bool-format-fix acl2::x)
           acl2::y)
      (char+short+int+long+llong+bool-format-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: char+short+int+long+llong+bool-format-equiv-of-char+short+int+long+llong+bool-format-fix-2-forward

(defthm
 char+short+int+long+llong+bool-format-equiv-of-char+short+int+long+llong+bool-format-fix-2-forward
 (implies
      (char+short+int+long+llong+bool-format-equiv
           acl2::x
           (char+short+int+long+llong+bool-format-fix acl2::y))
      (char+short+int+long+llong+bool-format-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)