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• Semantics

Numrep-match-repeat-range-p

Semantics of repetition ranges.

Signature

(numrep-match-repeat-range-p numrep range) → yes/no

Arguments

numrep — Guard (natp numrep).

range — Guard (repeat-rangep range).

Returns

yes/no — Type (booleanp yes/no).

A number of repetitions (a natural number) matches a repetition range iff it is between the range's minimum and the range's maximum.

Definitions and Theorems

Function: numrep-match-repeat-range-p

(defun numrep-match-repeat-range-p (numrep range)
  (declare (xargs :guard (and (natp numrep)
                              (repeat-rangep range))))
  (b* ((numrep (mbe :logic (nfix numrep) :exec numrep))
       (min (repeat-range->min range))
       (max (repeat-range->max range)))
    (and (<= min numrep)
         (or (nati-case max :infinity)
             (<= numrep (nati-finite->get max))))))

Theorem: booleanp-of-numrep-match-repeat-range-p

(defthm booleanp-of-numrep-match-repeat-range-p
  (b* ((yes/no (numrep-match-repeat-range-p numrep range)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: 0-when-match-repeat-range-0

(defthm 0-when-match-repeat-range-0
  (implies (equal range (repeat-range 0 (nati-finite 0)))
           (equal (numrep-match-repeat-range-p n range)
                  (equal (nfix n) 0))))

Theorem: numrep-match-repeat-range-p-of-nfix-numrep

(defthm numrep-match-repeat-range-p-of-nfix-numrep
  (equal (numrep-match-repeat-range-p (nfix numrep)
                                      range)
         (numrep-match-repeat-range-p numrep range)))

Theorem: numrep-match-repeat-range-p-nat-equiv-congruence-on-numrep

(defthm numrep-match-repeat-range-p-nat-equiv-congruence-on-numrep
  (implies (acl2::nat-equiv numrep numrep-equiv)
           (equal (numrep-match-repeat-range-p numrep range)
                  (numrep-match-repeat-range-p numrep-equiv range)))
  :rule-classes :congruence)

Theorem: numrep-match-repeat-range-p-of-repeat-range-fix-range

(defthm numrep-match-repeat-range-p-of-repeat-range-fix-range
  (equal
       (numrep-match-repeat-range-p numrep (repeat-range-fix range))
       (numrep-match-repeat-range-p numrep range)))

Theorem: numrep-match-repeat-range-p-repeat-range-equiv-congruence-on-range

(defthm
 numrep-match-repeat-range-p-repeat-range-equiv-congruence-on-range
 (implies (repeat-range-equiv range range-equiv)
          (equal (numrep-match-repeat-range-p numrep range)
                 (numrep-match-repeat-range-p numrep range-equiv)))
 :rule-classes :congruence)