Package list-filter-def: list-filter-def

Information

name	list-filter-def
version	1.11
description	list-filter-def
author	Joe Hurd <joe@gilith.com>
license	HOLLight
provenance	HOL Light theory extracted on 2011-09-21
show	Data.Bool

Files

Package tarball list-filter-def-1.11.tgz
Theory file list-filter-def.thy (included in the package tarball)

Defined Constant

Data
- List
  - Data.List.filter

Theorem

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

Input Type Operators

→
bool
Data
- List
  - Data.List.list

Input Constants

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

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

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

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