Package list-concat: Definitions and theorems about the list concat function
Information
| name | list-concat |
| version | 1.12 |
| description | Definitions and theorems about the list concat function |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| show | Data.Bool Data.List |
Files
- Package tarball list-concat-1.12.tgz
- Theory file list-concat.thy (included in the package tarball)
Defined Constant
- Data
- List
- concat
- List
Theorems
⊦ ∀l. null (concat l) ⇔ all null l
⊦ concat [] = [] ∧ ∀h t. concat (h :: t) = h @ concat t
Input Type Operators
- →
- bool
- Data
- List
- list
- List
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- F
- T
- List
- ::
- @
- []
- all
- null
- Bool
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
⊦ ∀l m. null (l @ m) ⇔ null l ∧ null m
⊦ (null [] ⇔ T) ∧ ∀h t. null (h :: t) ⇔ F
⊦ ∀P. P [] ∧ (∀a0 a1. P a1 ⇒ P (a0 :: a1)) ⇒ ∀x. P x
⊦ ∀NIL' CONS'.
∃fn. fn [] = NIL' ∧ ∀a0 a1. fn (a0 :: a1) = CONS' a0 a1 (fn a1)
⊦ (∀P. all P [] ⇔ T) ∧ ∀P h t. all P (h :: t) ⇔ P h ∧ all P t
⊦ ∀t. ((T ⇔ t) ⇔ t) ∧ ((t ⇔ T) ⇔ t) ∧ ((F ⇔ t) ⇔ ¬t) ∧ ((t ⇔ F) ⇔ ¬t)