Package list-zipwith-def: list-zipwith-def

Information

name	list-zipwith-def
version	1.14
description	list-zipwith-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-zipwith-def-1.14.tgz
Theory file list-zipwith-def.thy (included in the package tarball)

Defined Constant

Data
- List
  - Data.List.zipWith

Theorem

⊦ (∀f. Data.List.zipWith f Data.List.[] Data.List.[] = Data.List.[]) ∧
  ∀f h1 h2 t1 t2.
    Data.List.length t1 = Data.List.length t2 ⇒
    Data.List.zipWith f (Data.List.:: h1 t1) (Data.List.:: h2 t2) =
    Data.List.:: (f h1 h2) (Data.List.zipWith f t1 t2)

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.[]
  - Data.List.head
  - Data.List.length
  - Data.List.tail

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

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

⊦ ∀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)