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Substrings

Isubstrp

Case-insensitively test for the existence of a substring.

(isubstrp x y) determines if x ever occurs as a case-insensitive substring of y.

See also substrp for a case-sensitive version.

See also istrpos for an alternative that reports the position of the matched substring.

Definitions and Theorems

Function: isubstrp$inline

(defun isubstrp$inline (x y)
  (declare (type string x y))
  (if (istrpos x y) t nil))

Theorem: iprefixp-when-isubstrp

(defthm iprefixp-when-isubstrp
  (implies (isubstrp x y)
           (iprefixp (explode x)
                     (nthcdr (istrpos x y) (explode y)))))

Theorem: completeness-of-isubstrp

(defthm completeness-of-isubstrp
  (implies (and (iprefixp (explode x)
                          (nthcdr m (explode y)))
                (force (natp m)))
           (isubstrp x y)))

Theorem: istreqv-implies-equal-isubstrp-1

(defthm istreqv-implies-equal-isubstrp-1
  (implies (istreqv x x-equiv)
           (equal (isubstrp x y)
                  (isubstrp x-equiv y)))
  :rule-classes (:congruence))

Theorem: istreqv-implies-equal-isubstrp-2

(defthm istreqv-implies-equal-isubstrp-2
  (implies (istreqv y y-equiv)
           (equal (isubstrp x y)
                  (isubstrp x y-equiv)))
  :rule-classes (:congruence))