Package option-dest-thm: Properties of option type destructors
Information
| name | option-dest-thm |
| version | 1.9 |
| description | Properties of option type destructors |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2011-12-18 |
| requires | bool option-dest-def option-thm |
| show | Data.Bool Data.Option |
Files
- Package tarball option-dest-thm-1.9.tgz
- Theory file option-dest-thm.thy (included in the package tarball)
Theorem
⊦ ∀x. case none some x = x
Input Type Operators
- →
- bool
- Data
- Option
- option
- Option
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ⊤
- Option
- case
- none
- some
- Bool
Assumptions
⊦ ⊤
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀b f. case b f none = b
⊦ ∀x. x = none ∨ ∃a. x = some a
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀b f a. case b f (some a) = f a
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r