Package list-nub-def: list-nub-def

Information

name	list-nub-def
version	1.14
description	list-nub-def
author	Joe Hurd <joe@gilith.com>
license	HOLLight
provenance	HOL Light theory extracted on 2011-09-12
show	Data.Bool

Files

Package tarball list-nub-def-1.14.tgz
Theory file list-nub-def.thy (included in the package tarball)

Defined Constants

Data
- List
  - Data.List.nub
  - Data.List.nubReverse

Theorems

⊦ ∀l.
Data.List.nub l =
Data.List.reverse (Data.List.nubReverse (Data.List.reverse l))

⊦ Data.List.nubReverse Data.List.[] = Data.List.[] ∧
  ∀h t.
    Data.List.nubReverse (Data.List.:: h t) =
    if Data.List.member h t then Data.List.nubReverse t
    else Data.List.:: h (Data.List.nubReverse t)

Input Type Operators

→
bool
Data
- List
  - Data.List.list

Input Constants

=
select
Data
- Bool
  - ∀
  - ∧
  - ⇒
  - ∃
  - cond
  - T
- List
  - Data.List.::
  - Data.List.[]
  - Data.List.member
  - Data.List.reverse

Assumptions

⊦ T

⊦ (∃) = λP. P ((select) P)

⊦ (∀) = λp. p = λx. T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ ∀NIL' CONS'.
    ∃fn.
      fn Data.List.[] = NIL' ∧
      ∀a0 a1. fn (Data.List.:: a0 a1) = CONS' a0 a1 (fn a1)