Package list-concat-thm: list-concat-thm
Information
| name | list-concat-thm |
| version | 1.3 |
| description | list-concat-thm |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| show | Data.Bool |
Files
- Package tarball list-concat-thm-1.3.tgz
- Theory file list-concat-thm.thy (included in the package tarball)
Theorem
⊦ ∀l. Data.List.null (Data.List.concat l) ⇔ Data.List.all Data.List.null l
Input Type Operators
- →
- bool
- Data
- List
- Data.List.list
- List
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ¬
- F
- T
- List
- Data.List.::
- Data.List.@
- Data.List.[]
- Data.List.all
- Data.List.concat
- Data.List.null
- Bool
Assumptions
⊦ T
⊦ (∀) = λp. p = λx. T
⊦ ∀x. x = x ⇔ T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ ∀l m.
Data.List.null (Data.List.@ l m) ⇔ Data.List.null l ∧ Data.List.null m
⊦ (Data.List.null Data.List.[] ⇔ T) ∧
∀h t. Data.List.null (Data.List.:: h t) ⇔ F
⊦ Data.List.concat Data.List.[] = Data.List.[] ∧
∀h t.
Data.List.concat (Data.List.:: h t) =
Data.List.@ h (Data.List.concat t)
⊦ ∀P. P Data.List.[] ∧ (∀a0 a1. P a1 ⇒ P (Data.List.:: a0 a1)) ⇒ ∀x. P x
⊦ (∀P. Data.List.all P Data.List.[] ⇔ T) ∧
∀P h t. Data.List.all P (Data.List.:: h t) ⇔ P h ∧ Data.List.all P t
⊦ ∀t. ((T ⇔ t) ⇔ t) ∧ ((t ⇔ T) ⇔ t) ∧ ((F ⇔ t) ⇔ ¬t) ∧ ((t ⇔ F) ⇔ ¬t)