Package natural-numeral: Natural number numerals
Information
| name | natural-numeral |
| version | 1.8 |
| description | Natural number numerals |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| requires | bool natural-thm |
| show | Data.Bool Number.Natural |
Files
- Package tarball natural-numeral-1.8.tgz
- Theory file natural-numeral.thy (included in the package tarball)
Defined Constants
- Number
- Natural
- bit0
- bit1
- Natural
Theorems
⊦ bit0 0 = 0
⊦ ∀n. bit1 n = suc (bit0 n)
⊦ ∀n. bit0 (suc n) = suc (suc (bit0 n))
Input Type Operators
- →
- bool
- Number
- Natural
- natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- T
- Bool
- Number
- Natural
- 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. (∃) P ∧ ∀x y. P x ∧ P y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n