Package natural-numeral-def: Definition of natural number numerals
Information
| name | natural-numeral-def |
| version | 1.6 |
| description | Definition of natural number numerals |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| requires | bool natural-thm |
| show | Data.Bool Number.Natural |
Files
- Package tarball natural-numeral-def-1.6.tgz
- Theory source file natural-numeral-def.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))
External Type Operators
- →
- bool
- Number
- Natural
- natural
- Natural
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ⊤
- Bool
- Number
- Natural
- suc
- zero
- Natural
Assumptions
⊦ ⊤
⊦ ∀t. (λx. t x) = t
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. t ⇒ ⊤ ⇔ ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀p x. p x ⇒ p ((select) p)
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = 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