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Lhs.lisp

Svarlist-boundedp

(svarlist-boundedp x bound) recognizes lists where every element satisfies svar-boundedp.

Signature
(svarlist-boundedp x bound) → std::bool

This is an ordinary std::deflist. It is "loose" in that it does not care whether x is nil-terminated.

Definitions and Theorems

Function: svarlist-boundedp

(defun svarlist-boundedp (x bound)
  (declare (xargs :guard (and (svarlist-p x) (natp bound))))
  (let ((__function__ 'svarlist-boundedp))
    (declare (ignorable __function__))
    (if (consp x)
        (and (svar-boundedp (car x) bound)
             (svarlist-boundedp (cdr x) bound))
      t)))

Theorem: svarlist-boundedp-of-svarlist-fix-x

(defthm svarlist-boundedp-of-svarlist-fix-x
  (equal (svarlist-boundedp (svarlist-fix x)
                            bound)
         (svarlist-boundedp x bound)))

Theorem: svarlist-boundedp-svarlist-equiv-congruence-on-x

(defthm svarlist-boundedp-svarlist-equiv-congruence-on-x
  (implies (svarlist-equiv x x-equiv)
           (equal (svarlist-boundedp x bound)
                  (svarlist-boundedp x-equiv bound)))
  :rule-classes :congruence)

Theorem: svarlist-boundedp-of-nfix-bound

(defthm svarlist-boundedp-of-nfix-bound
  (equal (svarlist-boundedp x (nfix bound))
         (svarlist-boundedp x bound)))

Theorem: svarlist-boundedp-nat-equiv-congruence-on-bound

(defthm svarlist-boundedp-nat-equiv-congruence-on-bound
  (implies (nat-equiv bound bound-equiv)
           (equal (svarlist-boundedp x bound)
                  (svarlist-boundedp x bound-equiv)))
  :rule-classes :congruence)

Theorem: svarlist-boundedp-of-greater

(defthm svarlist-boundedp-of-greater
  (implies (and (svarlist-boundedp x bound1)
                (<= (nfix bound1) (nfix bound2)))
           (svarlist-boundedp x bound2)))

Subtopics

Svarlist-boundedp-basics: Basic theorems about svarlist-boundedp, generated by std::deflist.