Package list-member-def: list-member-def
Information
| name | list-member-def |
| version | 1.12 |
| description | list-member-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-member-def-1.12.tgz
- Theory file list-member-def.thy (included in the package tarball)
Defined Constant
- Data
- List
- Data.List.member
- List
Theorem
⊦ (∀x. Data.List.member x Data.List.[] ⇔ F) ∧
∀x h t.
Data.List.member x (Data.List.:: h t) ⇔ x = h ∨ Data.List.member x t
Input Type Operators
- →
- bool
- Data
- List
- Data.List.list
- List
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- F
- T
- List
- Data.List.::
- Data.List.[]
- Bool
Assumptions
⊦ T
⊦ (∃) = λP. P ((select) P)
⊦ (∀) = λp. p = λx. T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q
⊦ ∀NIL' CONS'.
∃fn.
fn Data.List.[] = NIL' ∧
∀a0 a1. fn (Data.List.:: a0 a1) = CONS' a0 a1 (fn a1)