Package natural-funpow-def: Definition of function power
Information
| name | natural-funpow-def |
| version | 1.11 |
| description | Definition of function power |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-12-02 |
| requires | bool function natural-thm |
| show | Data.Bool Function Number.Natural |
Files
- Package tarball natural-funpow-def-1.11.tgz
- Theory source file natural-funpow-def.thy (included in the package tarball)
Defined Constant
- Function
- ↑
Theorems
⊦ ∀f. f ↑ 0 = id
⊦ ∀f n. f ↑ suc n = f ∘ f ↑ n
External Type Operators
- →
- bool
- Number
- Natural
- natural
- Natural
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ⊤
- Bool
- Function
- id
- ∘
- Number
- Natural
- suc
- zero
- Natural
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀p. (∀x. ∃y. p x y) ⇔ ∃y. ∀x. p x (y x)
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n