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

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

Fixing function for char+short+int+long+llong+bool-format structures.

Signature

(char+short+int+long+llong+bool-format-fix x) → new-x

Arguments

x — Guard (char+short+int+long+llong+bool-formatp x).

Returns

new-x — Type (char+short+int+long+llong+bool-formatp new-x).

Definitions and Theorems

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

(defun char+short+int+long+llong+bool-format-fix$inline (x)
 (declare (xargs :guard (char+short+int+long+llong+bool-formatp x)))
 (mbe :logic
      (b* ((uchar (uchar-format-fix (cdr (std::da-nth 0 x))))
           (schar (schar-format-fix (cdr (std::da-nth 1 x))))
           (char (char-format-fix (cdr (std::da-nth 2 x))))
           (short (integer-format-fix (cdr (std::da-nth 3 x))))
           (int (integer-format-fix (cdr (std::da-nth 4 x))))
           (long (integer-format-fix (cdr (std::da-nth 5 x))))
           (llong (integer-format-fix (cdr (std::da-nth 6 x))))
           (bool (bool-format-fix (cdr (std::da-nth 7 x)))))
        (list (cons 'uchar uchar)
              (cons 'schar schar)
              (cons 'char char)
              (cons 'short short)
              (cons 'int int)
              (cons 'long long)
              (cons 'llong llong)
              (cons 'bool bool)))
      :exec x))

Theorem: char+short+int+long+llong+bool-formatp-of-char+short+int+long+llong+bool-format-fix

(defthm
 char+short+int+long+llong+bool-formatp-of-char+short+int+long+llong+bool-format-fix
 (b* ((new-x (char+short+int+long+llong+bool-format-fix$inline x)))
   (char+short+int+long+llong+bool-formatp new-x))
 :rule-classes :rewrite)

Theorem: char+short+int+long+llong+bool-format-fix-when-char+short+int+long+llong+bool-formatp

(defthm
 char+short+int+long+llong+bool-format-fix-when-char+short+int+long+llong+bool-formatp
 (implies (char+short+int+long+llong+bool-formatp x)
          (equal (char+short+int+long+llong+bool-format-fix x)
                 x)))

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)

Theorem: char+short+int+long+llong+bool-format-fix$inline-of-char+short+int+long+llong+bool-format-fix-x

(defthm
 char+short+int+long+llong+bool-format-fix$inline-of-char+short+int+long+llong+bool-format-fix-x
 (equal (char+short+int+long+llong+bool-format-fix$inline
             (char+short+int+long+llong+bool-format-fix x))
        (char+short+int+long+llong+bool-format-fix$inline x)))

Theorem: char+short+int+long+llong+bool-format-fix$inline-char+short+int+long+llong+bool-format-equiv-congruence-on-x

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