Package natural-min-max-def: natural-min-max-def
Information
| name | natural-min-max-def |
| version | 1.4 |
| description | natural-min-max-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-min-max-def-1.4.tgz
- Theory file natural-min-max-def.thy (included in the package tarball)
Defined Constants
- Number
- Natural
- Number.Natural.max
- Number.Natural.min
- Number.Natural.minimal
- Natural
Theorems
⊦ ∀m n. Number.Natural.max m n = if Number.Natural.≤ m n then n else m
⊦ ∀m n. Number.Natural.min m n = if Number.Natural.≤ m n then m else n
⊦ ∀P.
(∃n. P n) ⇔
P (Number.Natural.minimal P) ∧
∀m. Number.Natural.< m (Number.Natural.minimal P) ⇒ ¬P m
Input Type Operators
- →
- bool
- Number
- Natural
- Number.Natural.natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- cond
- T
- Bool
- Number
- Natural
- Number.Natural.<
- Number.Natural.≤
- Natural
Assumptions
⊦ T
⊦ (∃) = λP. P ((select) P)
⊦ (∀) = λp. p = λx. T
⊦ ∀x. x = x ⇔ T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ ∀P. (∃n. P n) ⇔ ∃n. P n ∧ ∀m. Number.Natural.< m n ⇒ ¬P m