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Acre-internals

Find-substr

Signature
(find-substr target x index) → pos
Arguments: target — Guard (stringp target).; x — Guard (stringp x).; index — Guard (natp index).
Returns: pos — Type (maybe-natp pos).

Definitions and Theorems

Function: find-substr

(defun find-substr (target x index)
  (declare (xargs :guard (and (stringp target)
                              (stringp x)
                              (natp index))))
  (declare (xargs :guard (<= index (strlen x))))
  (let ((__function__ 'find-substr))
    (declare (ignorable __function__))
    (str::strpos-fast (lstrfix target)
                      (lstrfix x)
                      (lnfix index)
                      (strlen target)
                      (strlen x))))

Theorem: maybe-natp-of-find-substr

(defthm maybe-natp-of-find-substr
  (b* ((pos (find-substr target x index)))
    (maybe-natp pos))
  :rule-classes :type-prescription)

Theorem: new-index-of-find-substr

(defthm new-index-of-find-substr
  (b* ((?pos (find-substr target x index)))
    (implies pos (<= (nfix index) pos)))
  :rule-classes :linear)

Theorem: new-index-of-find-substr-less-than-length

(defthm new-index-of-find-substr-less-than-length
  (b* ((?pos (find-substr target x index)))
    (implies (and pos
                  (<= (nfix index)
                      (len (acl2::explode x))))
             (<= pos
                 (- (len (acl2::explode x))
                    (len (acl2::explode target))))))
  :rule-classes :linear)

Theorem: find-substr-of-str-fix-target

(defthm find-substr-of-str-fix-target
  (equal (find-substr (acl2::str-fix target)
                      x index)
         (find-substr target x index)))

Theorem: find-substr-streqv-congruence-on-target

(defthm find-substr-streqv-congruence-on-target
  (implies (acl2::streqv target target-equiv)
           (equal (find-substr target x index)
                  (find-substr target-equiv x index)))
  :rule-classes :congruence)

Theorem: find-substr-of-str-fix-x

(defthm find-substr-of-str-fix-x
  (equal (find-substr target (acl2::str-fix x)
                      index)
         (find-substr target x index)))

Theorem: find-substr-streqv-congruence-on-x

(defthm find-substr-streqv-congruence-on-x
  (implies (acl2::streqv x x-equiv)
           (equal (find-substr target x index)
                  (find-substr target x-equiv index)))
  :rule-classes :congruence)

Theorem: find-substr-of-nfix-index

(defthm find-substr-of-nfix-index
  (equal (find-substr target x (nfix index))
         (find-substr target x index)))

Theorem: find-substr-nat-equiv-congruence-on-index

(defthm find-substr-nat-equiv-congruence-on-index
  (implies (acl2::nat-equiv index index-equiv)
           (equal (find-substr target x index)
                  (find-substr target x index-equiv)))
  :rule-classes :congruence)