Package option-dest-def: Definition of the option destructors

Information

Files

• Package tarball option-dest-def-1.0.tgz
• Theory file option-dest-def.thy (included in the package tarball)

Defined Constant

• Data
  • Option
    • Data.Option.case

Theorem

⊦ (∀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

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • select
    • T
  • Option
    • Data.Option.none
    • Data.Option.some

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