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Ascii-basic-source-char

Fixtype for ascii-basic-source-charp.

Definitions and Theorems

Function: ascii-basic-source-char-equiv$inline

(defun ascii-basic-source-char-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (ascii-basic-source-charp acl2::x)
                              (ascii-basic-source-charp acl2::y))))
  (equal (ascii-basic-source-char-fix acl2::x)
         (ascii-basic-source-char-fix acl2::y)))

Theorem: ascii-basic-source-char-equiv-is-an-equivalence

(defthm ascii-basic-source-char-equiv-is-an-equivalence
  (and (booleanp (ascii-basic-source-char-equiv x y))
       (ascii-basic-source-char-equiv x x)
       (implies (ascii-basic-source-char-equiv x y)
                (ascii-basic-source-char-equiv y x))
       (implies (and (ascii-basic-source-char-equiv x y)
                     (ascii-basic-source-char-equiv y z))
                (ascii-basic-source-char-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ascii-basic-source-char-equiv-implies-equal-ascii-basic-source-char-fix-1

(defthm
 ascii-basic-source-char-equiv-implies-equal-ascii-basic-source-char-fix-1
 (implies (ascii-basic-source-char-equiv acl2::x x-equiv)
          (equal (ascii-basic-source-char-fix acl2::x)
                 (ascii-basic-source-char-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: ascii-basic-source-char-fix-under-ascii-basic-source-char-equiv

(defthm
    ascii-basic-source-char-fix-under-ascii-basic-source-char-equiv
  (ascii-basic-source-char-equiv
       (ascii-basic-source-char-fix acl2::x)
       acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ascii-basic-source-char-fix-1-forward-to-ascii-basic-source-char-equiv

(defthm
 equal-of-ascii-basic-source-char-fix-1-forward-to-ascii-basic-source-char-equiv
 (implies (equal (ascii-basic-source-char-fix acl2::x)
                 acl2::y)
          (ascii-basic-source-char-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-ascii-basic-source-char-fix-2-forward-to-ascii-basic-source-char-equiv

(defthm
 equal-of-ascii-basic-source-char-fix-2-forward-to-ascii-basic-source-char-equiv
 (implies (equal acl2::x
                 (ascii-basic-source-char-fix acl2::y))
          (ascii-basic-source-char-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: ascii-basic-source-char-equiv-of-ascii-basic-source-char-fix-1-forward

(defthm
 ascii-basic-source-char-equiv-of-ascii-basic-source-char-fix-1-forward
 (implies (ascii-basic-source-char-equiv
               (ascii-basic-source-char-fix acl2::x)
               acl2::y)
          (ascii-basic-source-char-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: ascii-basic-source-char-equiv-of-ascii-basic-source-char-fix-2-forward

(defthm
 ascii-basic-source-char-equiv-of-ascii-basic-source-char-fix-2-forward
 (implies (ascii-basic-source-char-equiv
               acl2::x
               (ascii-basic-source-char-fix acl2::y))
          (ascii-basic-source-char-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)