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Maybe-backref-extract-substr

Signature

(maybe-backref-extract-substr x str) → substr

Arguments

x — Guard (maybe-backref-p x).

str — Guard (stringp str).

Returns

substr — Type (acl2::maybe-stringp substr).

Definitions and Theorems

Function: maybe-backref-extract-substr

(defun maybe-backref-extract-substr (x str)
  (declare (xargs :guard (and (maybe-backref-p x)
                              (stringp str))))
  (declare (xargs :guard (maybe-backref-in-bounds x str)))
  (let ((__function__ 'maybe-backref-extract-substr))
    (declare (ignorable __function__))
    (and x (backref-extract-substr x str))))

Theorem: maybe-stringp-of-maybe-backref-extract-substr

(defthm maybe-stringp-of-maybe-backref-extract-substr
  (b* ((substr (maybe-backref-extract-substr x str)))
    (acl2::maybe-stringp substr))
  :rule-classes :type-prescription)

Theorem: maybe-backref-extract-substr-exists

(defthm maybe-backref-extract-substr-exists
  (b* ((?substr (maybe-backref-extract-substr x str)))
    (iff substr x)))

Theorem: maybe-backref-extract-substr-is-string

(defthm maybe-backref-extract-substr-is-string
  (b* ((?substr (maybe-backref-extract-substr x str)))
    (iff (stringp substr) x)))

Theorem: maybe-backref-extract-substr-of-maybe-backref-fix-x

(defthm maybe-backref-extract-substr-of-maybe-backref-fix-x
  (equal (maybe-backref-extract-substr (maybe-backref-fix x)
                                       str)
         (maybe-backref-extract-substr x str)))

Theorem: maybe-backref-extract-substr-maybe-backref-equiv-congruence-on-x

(defthm
   maybe-backref-extract-substr-maybe-backref-equiv-congruence-on-x
  (implies (maybe-backref-equiv x x-equiv)
           (equal (maybe-backref-extract-substr x str)
                  (maybe-backref-extract-substr x-equiv str)))
  :rule-classes :congruence)

Theorem: maybe-backref-extract-substr-of-str-fix-str

(defthm maybe-backref-extract-substr-of-str-fix-str
  (equal (maybe-backref-extract-substr x (acl2::str-fix str))
         (maybe-backref-extract-substr x str)))

Theorem: maybe-backref-extract-substr-streqv-congruence-on-str

(defthm maybe-backref-extract-substr-streqv-congruence-on-str
  (implies (acl2::streqv str str-equiv)
           (equal (maybe-backref-extract-substr x str)
                  (maybe-backref-extract-substr x str-equiv)))
  :rule-classes :congruence)