Constrained recognizer and fixer and mappings, and fixtype, for the execution character set.
These are analogous to the ones for the source character set. See source-char-recognizer+fixer+mappings+fixtype.
Theorem:
(defthm booleanp-of-exec-charp (booleanp (exec-charp x)) :rule-classes :type-prescription)
Theorem:
(defthm exec-charp-of-exec-char-fix (exec-charp (exec-char-fix x)))
Theorem:
(defthm exec-char-fix-when-exec-charp (implies (exec-charp x) (equal (exec-char-fix x) x)))
Theorem:
(defthm ascii-to-exec-char-of-ascii-basic-exec-char-fix (equal (ascii-to-exec-char (ascii-basic-exec-char-fix x)) (ascii-to-exec-char x)))
Theorem:
(defthm exec-charp-of-ascii-to-exec-char (exec-charp (ascii-to-exec-char x)))
Theorem:
(defthm ascii-to-exec-char-injective (equal (equal (ascii-to-exec-char x) (ascii-to-exec-char y)) (ascii-basic-exec-char-equiv x y)))
Theorem:
(defthm exec-char-to-number-of-exec-char-fix (equal (exec-char-to-number (exec-char-fix x)) (exec-char-to-number x)))
Theorem:
(defthm natp-of-exec-char-to-number (natp (exec-char-to-number x)) :rule-classes :type-prescription)
Theorem:
(defthm exec-char-to-number-injective-lemma (equal (equal (exec-char-to-number x) (exec-char-to-number y)) (equal (exec-char-fix x) (exec-char-fix y))))
Theorem:
(defthm posp-of-exec-char-to-number-bound (posp (exec-char-to-number-bound)) :rule-classes :type-prescription)
Theorem:
(defthm exec-char-to-number-below-bound (< (exec-char-to-number x) (exec-char-to-number-bound)) :rule-classes :linear)
Function:
(defun exec-char-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (exec-charp acl2::x) (exec-charp acl2::y)))) (equal (exec-char-fix acl2::x) (exec-char-fix acl2::y)))
Theorem:
(defthm exec-char-equiv-is-an-equivalence (and (booleanp (exec-char-equiv x y)) (exec-char-equiv x x) (implies (exec-char-equiv x y) (exec-char-equiv y x)) (implies (and (exec-char-equiv x y) (exec-char-equiv y z)) (exec-char-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm exec-char-equiv-implies-equal-exec-char-fix-1 (implies (exec-char-equiv acl2::x x-equiv) (equal (exec-char-fix acl2::x) (exec-char-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm exec-char-fix-under-exec-char-equiv (exec-char-equiv (exec-char-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-exec-char-fix-1-forward-to-exec-char-equiv (implies (equal (exec-char-fix acl2::x) acl2::y) (exec-char-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-exec-char-fix-2-forward-to-exec-char-equiv (implies (equal acl2::x (exec-char-fix acl2::y)) (exec-char-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm exec-char-equiv-of-exec-char-fix-1-forward (implies (exec-char-equiv (exec-char-fix acl2::x) acl2::y) (exec-char-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm exec-char-equiv-of-exec-char-fix-2-forward (implies (exec-char-equiv acl2::x (exec-char-fix acl2::y)) (exec-char-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm exec-char-to-number-injective (equal (equal (exec-char-to-number x) (exec-char-to-number y)) (exec-char-equiv x y)))
Theorem:
(defthm ascii-to-exec-char-of-ascii-basic-exec-char-fix-x (equal (ascii-to-exec-char (ascii-basic-exec-char-fix x)) (ascii-to-exec-char x)))
Theorem:
(defthm ascii-to-exec-char-ascii-basic-exec-char-equiv-congruence-on-x (implies (ascii-basic-exec-char-equiv x x-equiv) (equal (ascii-to-exec-char x) (ascii-to-exec-char x-equiv))) :rule-classes :congruence)
Theorem:
(defthm exec-char-to-number-of-exec-char-fix-x (equal (exec-char-to-number (exec-char-fix x)) (exec-char-to-number x)))
Theorem:
(defthm exec-char-to-number-exec-char-equiv-congruence-on-x (implies (exec-char-equiv x x-equiv) (equal (exec-char-to-number x) (exec-char-to-number x-equiv))) :rule-classes :congruence)