Package list-nth-def: list-nth-def

Information

name	list-nth-def
version	1.12
description	list-nth-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-nth-def-1.12.tgz
Theory file list-nth-def.thy (included in the package tarball)

Defined Constant

Data
- List
  - Data.List.nth

Theorem

⊦ (∀h t. Data.List.nth 0 (Data.List.:: h t) = h) ∧
  ∀h t n.
    Number.Natural.< n (Data.List.length t) ⇒
    Data.List.nth (Number.Natural.suc n) (Data.List.:: h t) =
    Data.List.nth n t

Input Type Operators

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

Input Constants

=
select
Data
- Bool
  - ∀
  - ∧
  - ⇒
  - ∃
  - ~
  - F
  - T
- List
  - Data.List.::
  - Data.List.head
  - Data.List.length
  - Data.List.tail
Number
- Natural
  - Number.Natural.<
  - Number.Natural.suc
  - Number.Natural.zero

Assumptions

⊦ T

⊦ (∃) = λP. P ((select) P)

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λp. p = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀h t. Data.List.head (Data.List.:: h t) = h

⊦ ∀h t. Data.List.tail (Data.List.:: h t) = t

⊦ (∧) = 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

⊦ ∀t. (T ∧ t ⇔ t) ∧ (t ∧ T ⇔ t) ∧ (F ∧ t ⇔ F) ∧ (t ∧ F ⇔ F) ∧ (t ∧ t ⇔ t)

⊦ ∀t. (T ⇒ t ⇔ t) ∧ (t ⇒ T ⇔ T) ∧ (F ⇒ t ⇔ T) ∧ (t ⇒ t ⇔ T) ∧ (t ⇒ F ⇔ ¬t)