Package list-replicate-def: Definition of the list replicate function
Information
| name | list-replicate-def |
| version | 1.31 |
| description | Definition of the list replicate function |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2012-02-10 |
| requires | bool natural |
| show | Data.Bool Data.List Number.Natural |
Files
- Package tarball list-replicate-def-1.31.tgz
- Theory file list-replicate-def.thy (included in the package tarball)
Defined Constant
- Data
- List
- replicate
- List
Theorems
⊦ ∀x. replicate 0 x = []
⊦ ∀x n. replicate (suc n) x = x :: replicate n x
Input Type Operators
- →
- bool
- Data
- List
- list
- List
- Number
- Natural
- natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ⊤
- List
- ::
- []
- Bool
- Number
- Natural
- suc
- zero
- Natural
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀p. (∀x. ∃y. p x y) ⇔ ∃y. ∀x. p x (y x)
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n