Package sum-thm: Properties of sum types
Information
| name | sum-thm |
| version | 1.1 |
| description | Properties of sum types |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-11-09 |
| checksum | 01fd163ede0704e34ff00760c9bb8182f4e51762 |
| requires | bool sum-def |
| show | Data.Bool Data.Sum |
Files
- Package tarball sum-thm-1.1.tgz
- Theory source file sum-thm.thy (included in the package tarball)
Theorems
⊦ ∀x. case left right x = x
⊦ ∀x. (∃a. x = left a) ∨ ∃b. x = right b
⊦ ∀f g x. isLeft x ⇒ case f g x = f (destLeft x)
⊦ ∀f g x. isRight x ⇒ case f g x = g (destRight x)
External Type Operators
- →
- bool
- Data
- Sum
- +
- Sum
External Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- ⊥
- ⊤
- Sum
- case
- destLeft
- destRight
- isLeft
- isRight
- left
- right
- Bool
Assumptions
⊦ ⊤
⊦ ∀a. isLeft (left a)
⊦ ∀b. isRight (right b)
⊦ ⊥ ⇔ ∀p. p
⊦ ∀a. ¬isRight (left a)
⊦ ∀b. ¬isLeft (right b)
⊦ (¬) = λp. p ⇒ ⊥
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀a. destLeft (left a) = a
⊦ ∀b. destRight (right b) = b
⊦ ∀t. ⊥ ⇒ t ⇔ ⊤
⊦ ∀t. ⊤ ⇒ t ⇔ t
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀f g a. case f g (left a) = f a
⊦ ∀f g b. case f g (right b) = g b
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀p. (∀a. p (left a)) ∧ (∀b. p (right b)) ⇒ ∀x. p x