Package natural-numeral-def: natural-numeral-def

Information

name	natural-numeral-def
version	1.4
description	natural-numeral-def
author	Joe Hurd <joe@gilith.com>
license	HOLLight
provenance	HOL Light theory extracted on 2011-07-25
show	Data.Bool

Files

Package tarball natural-numeral-def-1.4.tgz
Theory file natural-numeral-def.thy (included in the package tarball)

Defined Constants

Number
- Natural
  - Number.Natural.bit0
  - Number.Natural.bit1

Theorems

⊦ ∀n. Number.Natural.bit1 n = Number.Natural.suc (Number.Natural.bit0 n)

⊦ Number.Natural.bit0 0 = 0 ∧
  ∀n.
    Number.Natural.bit0 (Number.Natural.suc n) =
    Number.Natural.suc (Number.Natural.suc (Number.Natural.bit0 n))

Input Type Operators

→
bool
Number
- Natural
  - Number.Natural.natural

Input Constants

=
select
Data
- Bool
  - ∀
  - ∧
  - ⇒
  - ∃
  - T
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

⊦ ∀e f. ∃fn. fn 0 = e ∧ ∀n. fn (Number.Natural.suc n) = f (fn n) n