Package option-dest-def: Definition of the option destructors
Information
| name | option-dest-def |
| version | 1.17 |
| description | Definition of the option destructors |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| show | Data.Bool |
Files
- Package tarball option-dest-def-1.17.tgz
- Theory file option-dest-def.thy (included in the package tarball)
Defined Constants
- Data
- Option
- Data.Option.case
- Data.Option.isNone
- Data.Option.isSome
- Option
Theorems
⊦ (Data.Option.isNone Data.Option.none ⇔ T) ∧
∀a. Data.Option.isNone (Data.Option.some a) ⇔ F
⊦ (Data.Option.isSome Data.Option.none ⇔ F) ∧
∀a. Data.Option.isSome (Data.Option.some a) ⇔ T
⊦ (∀b f. Data.Option.case b f Data.Option.none = b) ∧
∀b f a. Data.Option.case b f (Data.Option.some a) = f a
Input Type Operators
- →
- bool
- Data
- Option
- Data.Option.option
- Option
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- F
- T
- Option
- Data.Option.none
- Data.Option.some
- 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
⊦ ∀NONE' SOME'.
∃fn.
fn Data.Option.none = NONE' ∧ ∀a. fn (Data.Option.some a) = SOME' a