Package natural-add-numeral: natural-add-numeral

Information

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

Files

Package tarball natural-add-numeral-1.0.tgz
Theory file natural-add-numeral.thy (included in the package tarball)

Theorems

⊦ ∀n. Number.Numeral.bit0 n = Number.Natural.+ n n

⊦ ∀n. Number.Numeral.bit1 n = Number.Natural.suc (Number.Natural.+ n n)

Input Type Operators

→
bool
Number
- Natural
  - Number.Natural.natural

Input Constants

=
Data
- Bool
  - ∀
  - ∧
  - ⇒
  - T
Number
- Natural
  - Number.Natural.+
  - Number.Natural.suc
- Numeral
  - Number.Numeral.bit0
  - Number.Numeral.bit1
  - Number.Numeral.zero

Assumptions

⊦ T

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

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

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

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

⊦ ∀P.
P Number.Numeral.zero ∧ (∀n. P n ⇒ P (Number.Natural.suc n)) ⇒ ∀n. P n

⊦ (∀n. Number.Natural.+ Number.Numeral.zero n = n) ∧
  (∀m. Number.Natural.+ m Number.Numeral.zero = m) ∧
  (∀m n.
     Number.Natural.+ (Number.Natural.suc m) n =
     Number.Natural.suc (Number.Natural.+ m n)) ∧
  ∀m n.
    Number.Natural.+ m (Number.Natural.suc n) =
    Number.Natural.suc (Number.Natural.+ m n)