Package unit-thm: Properties of the unit type
Information
| name | unit-thm |
| version | 1.3 |
| description | Properties of the unit type |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| requires | bool unit-def |
| show | Data.Bool Data.Unit |
Files
- Package tarball unit-thm-1.3.tgz
- Theory file unit-thm.thy (included in the package tarball)
Theorems
⊦ ∀f g. f = g
⊦ ∀e. ∃fn. fn () = e
⊦ ∀e. ∃!fn. fn () = e
⊦ ∀P. P () ⇒ ∀x. P x
Input Type Operators
- →
- bool
- Data
- Unit
- unit
- Unit
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ¬
- F
- T
- Unit
- ()
- Bool
Assumptions
⊦ T
⊦ ∀v. v = ()
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. T
⊦ ∀x. x = x ⇔ T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q
⊦ ∀f g. f = g ⇔ ∀x. f x = g x
⊦ ∀P. (∃!x. P x) ⇔ (∃x. P x) ∧ ∀x x'. P x ∧ P x' ⇒ x = x'
⊦ ∀t. (T ∧ t ⇔ t) ∧ (t ∧ T ⇔ t) ∧ (F ∧ t ⇔ F) ∧ (t ∧ F ⇔ F) ∧ (t ∧ t ⇔ t)
⊦ ∀t. (T ⇒ t ⇔ t) ∧ (t ⇒ T ⇔ T) ∧ (F ⇒ t ⇔ T) ∧ (t ⇒ t ⇔ T) ∧ (t ⇒ F ⇔ ¬t)