Package list-interval-def: list-interval-def

Information

name	list-interval-def
version	1.0
description	list-interval-def
author	Joe Hurd <joe@gilith.com>
license	HOLLight
provenance	HOL Light theory extracted on 2011-02-19
show	Data.Bool

Files

Package tarball list-interval-def-1.0.tgz
Theory file list-interval-def.thy (included in the package tarball)

Defined Constant

Data
- List
  - Data.List.interval

Theorem

⊦ (∀m. Data.List.interval m Number.Numeral.zero = Data.List.[]) ∧
  ∀m n.
    Data.List.interval m (Number.Natural.suc n) =
    Data.List.:: m (Data.List.interval (Number.Natural.suc m) n)

Input Type Operators

→
bool
Data
- List
  - Data.List.list
Number
- Natural
  - Number.Natural.natural

Input Constants

=
Data
- Bool
  - ∀
  - ∧
  - ⇒
  - ∃
  - select
  - T
- List
  - Data.List.::
  - Data.List.[]
Number
- Natural
  - Number.Natural.suc
- Numeral
  - Number.Numeral.zero

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

⊦ ∀e f.
    ∃fn.
      fn Number.Numeral.zero = e ∧
      ∀n. fn (Number.Natural.suc n) = f (fn n) n