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Num-range

Num-range->base

Get the base field from a num-range.

Signature
(num-range->base x) → base
Arguments: x — Guard (num-range-p x).
Returns: base — Type (num-base-p base).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: num-range->base$inline

(defun num-range->base$inline (x)
  (declare (xargs :guard (num-range-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'num-range->base))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (num-base-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: num-base-p-of-num-range->base

(defthm num-base-p-of-num-range->base
  (b* ((base (num-range->base$inline x)))
    (num-base-p base))
  :rule-classes :rewrite)

Theorem: num-range->base$inline-of-num-range-fix-x

(defthm num-range->base$inline-of-num-range-fix-x
  (equal (num-range->base$inline (num-range-fix x))
         (num-range->base$inline x)))

Theorem: num-range->base$inline-num-range-equiv-congruence-on-x

(defthm num-range->base$inline-num-range-equiv-congruence-on-x
  (implies (num-range-equiv x x-equiv)
           (equal (num-range->base$inline x)
                  (num-range->base$inline x-equiv)))
  :rule-classes :congruence)