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Types

Type-arithmetic-listp

Check if a list of types consists of all arithmetic types.

Signature
(type-arithmetic-listp x) → 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: type-arithmetic-listp

(defun type-arithmetic-listp (x)
  (declare (xargs :guard (type-listp x)))
  (let ((__function__ 'type-arithmetic-listp))
    (declare (ignorable __function__))
    (if (consp x)
        (and (type-arithmeticp (car x))
             (type-arithmetic-listp (cdr x)))
      t)))

Theorem: type-arithmetic-listp-of-type-list-fix-x

(defthm type-arithmetic-listp-of-type-list-fix-x
  (equal (type-arithmetic-listp (type-list-fix x))
         (type-arithmetic-listp x)))

Theorem: type-arithmetic-listp-type-list-equiv-congruence-on-x

(defthm type-arithmetic-listp-type-list-equiv-congruence-on-x
  (implies (type-list-equiv x x-equiv)
           (equal (type-arithmetic-listp x)
                  (type-arithmetic-listp x-equiv)))
  :rule-classes :congruence)

Subtopics

Type-arithmetic-listp-basics: Basic theorems about type-arithmetic-listp, generated by std::deflist.