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Vl-simple-id-tail-string-p

Signature

(vl-simple-id-tail-string-p x i len) → *

Arguments

x — Guard (stringp x).

i — Guard (natp i).

len — Guard (eql len (length x)).

Definitions and Theorems

Function: vl-simple-id-tail-string-p

(defun vl-simple-id-tail-string-p (x i len)
  (declare (xargs :guard (and (stringp x)
                              (natp i)
                              (eql len (length x)))))
  (declare (xargs :guard (<= i len)))
  (let ((__function__ 'vl-simple-id-tail-string-p))
    (declare (ignorable __function__))
    (if (mbe :logic (zp (- (nfix len) (nfix i)))
             :exec (eql i len))
        t
      (and (vl-simple-id-tail-p (char x i))
           (vl-simple-id-tail-string-p x (+ 1 (lnfix i))
                                       len)))))

Theorem: vl-simple-id-tail-string-p-of-str-fix-x

(defthm vl-simple-id-tail-string-p-of-str-fix-x
  (equal (vl-simple-id-tail-string-p (str-fix x)
                                     i len)
         (vl-simple-id-tail-string-p x i len)))

Theorem: vl-simple-id-tail-string-p-streqv-congruence-on-x

(defthm vl-simple-id-tail-string-p-streqv-congruence-on-x
  (implies (streqv x x-equiv)
           (equal (vl-simple-id-tail-string-p x i len)
                  (vl-simple-id-tail-string-p x-equiv i len)))
  :rule-classes :congruence)

Theorem: vl-simple-id-tail-string-p-of-nfix-i

(defthm vl-simple-id-tail-string-p-of-nfix-i
  (equal (vl-simple-id-tail-string-p x (nfix i)
                                     len)
         (vl-simple-id-tail-string-p x i len)))

Theorem: vl-simple-id-tail-string-p-nat-equiv-congruence-on-i

(defthm vl-simple-id-tail-string-p-nat-equiv-congruence-on-i
  (implies (acl2::nat-equiv i i-equiv)
           (equal (vl-simple-id-tail-string-p x i len)
                  (vl-simple-id-tail-string-p x i-equiv len)))
  :rule-classes :congruence)