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• Fresh-ident-utility

Make-numbered-string

Signature

(make-numbered-string base number-prefix number number-suffix) 
  → 
string

Arguments

base — Guard (stringp base).

number-prefix — Guard (stringp number-prefix).

number — Guard (natp number).

number-suffix — Guard (stringp number-suffix).

Returns

string — Type (stringp string).

Definitions and Theorems

Function: make-numbered-string

(defun make-numbered-string
       (base number-prefix number number-suffix)
  (declare (xargs :guard (and (stringp base)
                              (stringp number-prefix)
                              (natp number)
                              (stringp number-suffix))))
  (concatenate
       'string
       (mbe :logic (acl2::str-fix base)
            :exec base)
       (mbe :logic (acl2::str-fix number-prefix)
            :exec number-prefix)
       (acl2::implode (explode-nonnegative-integer
                           (mbe :logic (nfix number) :exec number)
                           10 nil))
       (mbe :logic (acl2::str-fix number-suffix)
            :exec number-suffix)))

Theorem: stringp-of-make-numbered-string

(defthm stringp-of-make-numbered-string
  (b*
   ((string
         (make-numbered-string base
                               number-prefix number number-suffix)))
   (stringp string))
  :rule-classes :rewrite)

Theorem: make-numbered-string-of-str-fix-base

(defthm make-numbered-string-of-str-fix-base
  (equal (make-numbered-string (acl2::str-fix base)
                               number-prefix number number-suffix)
         (make-numbered-string base
                               number-prefix number number-suffix)))

Theorem: make-numbered-string-streqv-congruence-on-base

(defthm make-numbered-string-streqv-congruence-on-base
 (implies
  (acl2::streqv base base-equiv)
  (equal
      (make-numbered-string base number-prefix number number-suffix)
      (make-numbered-string base-equiv
                            number-prefix number number-suffix)))
 :rule-classes :congruence)

Theorem: make-numbered-string-of-str-fix-number-prefix

(defthm make-numbered-string-of-str-fix-number-prefix
  (equal (make-numbered-string base (acl2::str-fix number-prefix)
                               number number-suffix)
         (make-numbered-string base
                               number-prefix number number-suffix)))

Theorem: make-numbered-string-streqv-congruence-on-number-prefix

(defthm make-numbered-string-streqv-congruence-on-number-prefix
 (implies
  (acl2::streqv number-prefix number-prefix-equiv)
  (equal
      (make-numbered-string base number-prefix number number-suffix)
      (make-numbered-string base number-prefix-equiv
                            number number-suffix)))
 :rule-classes :congruence)

Theorem: make-numbered-string-of-nfix-number

(defthm make-numbered-string-of-nfix-number
  (equal (make-numbered-string base number-prefix (nfix number)
                               number-suffix)
         (make-numbered-string base
                               number-prefix number number-suffix)))

Theorem: make-numbered-string-nat-equiv-congruence-on-number

(defthm make-numbered-string-nat-equiv-congruence-on-number
 (implies
  (acl2::nat-equiv number number-equiv)
  (equal
      (make-numbered-string base number-prefix number number-suffix)
      (make-numbered-string base number-prefix
                            number-equiv number-suffix)))
 :rule-classes :congruence)

Theorem: make-numbered-string-of-str-fix-number-suffix

(defthm make-numbered-string-of-str-fix-number-suffix
  (equal (make-numbered-string base number-prefix
                               number (acl2::str-fix number-suffix))
         (make-numbered-string base
                               number-prefix number number-suffix)))

Theorem: make-numbered-string-streqv-congruence-on-number-suffix

(defthm make-numbered-string-streqv-congruence-on-number-suffix
 (implies
  (acl2::streqv number-suffix number-suffix-equiv)
  (equal
      (make-numbered-string base number-prefix number number-suffix)
      (make-numbered-string base number-prefix
                            number number-suffix-equiv)))
 :rule-classes :congruence)