Package list-quant-def: list-quant-def
Information
| name | list-quant-def |
| version | 1.11 |
| description | list-quant-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-quant-def-1.11.tgz
- Theory file list-quant-def.thy (included in the package tarball)
Defined Constants
- Data
- List
- Data.List.all
- Data.List.exists
- List
Theorems
⊦ (∀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
⊦ (∀P. Data.List.exists P Data.List.[] ⇔ F) ∧
∀P h t.
Data.List.exists P (Data.List.:: h t) ⇔ P h ∨ Data.List.exists P 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)