Package list-nth-def: list-nth-def
Information
| name | list-nth-def |
| version | 1.13 |
| description | list-nth-def |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| show | Data.Bool |
Files
- Package tarball list-nth-def-1.13.tgz
- Theory file list-nth-def.thy (included in the package tarball)
Defined Constant
- Data
- List
- Data.List.nth
- List
Theorem
⊦ (∀h t. Data.List.nth 0 (Data.List.:: h t) = h) ∧
∀h t n.
Number.Natural.< n (Data.List.length t) ⇒
Data.List.nth (Number.Natural.suc n) (Data.List.:: h t) =
Data.List.nth n t
Input Type Operators
- →
- bool
- Data
- List
- Data.List.list
- List
- Number
- Natural
- Number.Natural.natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- F
- T
- List
- Data.List.::
- Data.List.head
- Data.List.length
- Data.List.tail
- Bool
- Number
- Natural
- Number.Natural.<
- Number.Natural.suc
- Number.Natural.zero
- Natural
Assumptions
⊦ T
⊦ (∃) = λP. P ((select) P)
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. T
⊦ ∀x. x = x ⇔ T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀h t. Data.List.head (Data.List.:: h t) = h
⊦ ∀h t. Data.List.tail (Data.List.:: h t) = t
⊦ (∧) = 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
⊦ ∀t. (T ∧ t ⇔ t) ∧ (t ∧ T ⇔ t) ∧ (F ∧ t ⇔ F) ∧ (t ∧ F ⇔ F) ∧ (t ∧ t ⇔ t)
⊦ ∀t. (T ⇒ t ⇔ t) ∧ (t ⇒ T ⇔ T) ∧ (F ⇒ t ⇔ T) ∧ (t ⇒ t ⇔ T) ∧ (t ⇒ F ⇔ ¬t)