Package list-concat-thm: Properties of the list concat function
Information
| name | list-concat-thm |
| version | 1.8 |
| description | Properties of the list concat function |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-11-15 |
| requires | bool list-def list-dest list-append list-quant list-concat-def |
| show | Data.Bool Data.List |
Files
- Package tarball list-concat-thm-1.8.tgz
- Theory file list-concat-thm.thy (included in the package tarball)
Theorem
⊦ ∀l. null (concat l) ⇔ all null l
Input Type Operators
- →
- bool
- Data
- List
- list
- List
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- T
- List
- ::
- @
- []
- all
- concat
- null
- Bool
Assumptions
⊦ T
⊦ null []
⊦ concat [] = []
⊦ ∀p. all p []
⊦ (∀) = λp. p = λx. T
⊦ ∀t. (T ⇔ t) ⇔ t
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ ∀h t. concat (h :: t) = h @ concat t
⊦ ∀l m. null (l @ m) ⇔ null l ∧ null m
⊦ ∀p h t. all p (h :: t) ⇔ p h ∧ all p t
⊦ ∀P. P [] ∧ (∀a0 a1. P a1 ⇒ P (a0 :: a1)) ⇒ ∀x. P x