Package option-dest-thm: option-dest-thm

Information

Files

• Package tarball option-dest-thm-1.2.tgz
• Theory file option-dest-thm.thy (included in the package tarball)

Theorem

⊦ ∀x. Data.Option.case.none.some Data.Option.none Data.Option.some x = x

Input Type Operators

• →
• bool
• Data
  • Option
    • Data.Option.option

Input Constants

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

Assumptions

⊦ T

⊦ (∀) = λp. p = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀x. x = Data.Option.none ∨ ∃a. x = Data.Option.some a

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r

⊦ (∀b f. Data.Option.case.none.some b f Data.Option.none = b) ∧
  ∀b f a. Data.Option.case.none.some b f (Data.Option.some a) = f a