Package list-replicate-def: list-replicate-def

Information

name	list-replicate-def
version	1.12
description	list-replicate-def
author	Joe Hurd <joe@gilith.com>
license	HOLLight
provenance	HOL Light theory extracted on 2011-07-25
show	Data.Bool

Files

Package tarball list-replicate-def-1.12.tgz
Theory file list-replicate-def.thy (included in the package tarball)

Defined Constant

Data
- List
  - Data.List.replicate

Theorem

⊦ (∀x. Data.List.replicate 0 x = Data.List.[]) ∧
  ∀x n.
    Data.List.replicate (Number.Natural.suc n) x =
    Data.List.:: x (Data.List.replicate n x)

Input Type Operators

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

Input Constants

=
select
Data
- Bool
  - ∀
  - ∧
  - ⇒
  - ∃
  - T
- List
  - Data.List.::
  - Data.List.[]
Number
- Natural
  - Number.Natural.suc
  - Number.Natural.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 0 = e ∧ ∀n. fn (Number.Natural.suc n) = f (fn n) n