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Grammar

Cst-%x30-39-nat

Signature
(cst-%x30-39-nat abnf::cst) → nat
Arguments: abnf::cst — Guard (abnf::treep abnf::cst).
Returns: nat — Type (natp nat).

Definitions and Theorems

Function: cst-%x30-39-nat

(defun cst-%x30-39-nat (abnf::cst)
  (declare (xargs :guard (abnf::treep abnf::cst)))
  (declare (xargs :guard (cst-matchp abnf::cst "%x30-39")))
  (let ((__function__ 'cst-%x30-39-nat))
    (declare (ignorable __function__))
    (lnfix (nth 0
                (abnf::tree-leafterm->get abnf::cst)))))

Theorem: natp-of-cst-%x30-39-nat

(defthm natp-of-cst-%x30-39-nat
  (b* ((nat (cst-%x30-39-nat abnf::cst)))
    (natp nat))
  :rule-classes :rewrite)

Theorem: cst-%x30-39-nat-of-tree-fix-cst

(defthm cst-%x30-39-nat-of-tree-fix-cst
  (equal (cst-%x30-39-nat (abnf::tree-fix abnf::cst))
         (cst-%x30-39-nat abnf::cst)))

Theorem: cst-%x30-39-nat-tree-equiv-congruence-on-cst

(defthm cst-%x30-39-nat-tree-equiv-congruence-on-cst
  (implies (abnf::tree-equiv abnf::cst cst-equiv)
           (equal (cst-%x30-39-nat abnf::cst)
                  (cst-%x30-39-nat cst-equiv)))
  :rule-classes :congruence)