Package natural-order-def: natural-order-def
Information
| name | natural-order-def |
| version | 1.5 |
| description | natural-order-def |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| show | Data.Bool |
Files
- Package tarball natural-order-def-1.5.tgz
- Theory file natural-order-def.thy (included in the package tarball)
Defined Constants
- Number
- Natural
- Number.Natural.<
- Number.Natural.≤
- Number.Natural.>
- Number.Natural.≥
- Natural
Theorems
⊦ ∀n m. Number.Natural.> m n ⇔ Number.Natural.< n m
⊦ ∀n m. Number.Natural.≥ m n ⇔ Number.Natural.≤ n m
⊦ (∀m. Number.Natural.< m 0 ⇔ F) ∧
∀m n.
Number.Natural.< m (Number.Natural.suc n) ⇔
m = n ∨ Number.Natural.< m n
⊦ (∀m. Number.Natural.≤ m 0 ⇔ m = 0) ∧
∀m n.
Number.Natural.≤ m (Number.Natural.suc n) ⇔
m = Number.Natural.suc n ∨ Number.Natural.≤ m n
Input Type Operators
- →
- bool
- Number
- Natural
- Number.Natural.natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- F
- T
- Bool
- Number
- Natural
- Number.Natural.suc
- Number.Natural.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
⊦ ∀e f. ∃fn. fn 0 = e ∧ ∀n. fn (Number.Natural.suc n) = f (fn n) n