Package natural-exp-def: Definition of natural number exponentiation
Information
| name | natural-exp-def |
| version | 1.13 |
| description | Definition of natural number exponentiation |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-11-27 |
| requires | bool natural-thm |
| show | Data.Bool Number.Natural |
Files
- Package tarball natural-exp-def-1.13.tgz
- Theory file natural-exp-def.thy (included in the package tarball)
Defined Constant
- Number
- Natural
- exp
- Natural
Theorems
⊦ ∀m. exp m 0 = 1
⊦ ∀m n. exp m (suc n) = m * exp m n
Input Type Operators
- →
- bool
- Number
- Natural
- natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- T
- Bool
- Number
- Natural
- *
- bit1
- suc
- zero
- Natural
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
⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q
⊦ (∃!) = λP. (∃) P ∧ ∀x y. P x ∧ P y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n