Package pair-induct: pair-induct

Information

Files

• Package tarball pair-induct-1.0.tgz
• Theory file pair-induct.thy (included in the package tarball)

Theorems

⊦ ∀x. Data.Pair., (Data.Pair.fst x) (Data.Pair.snd x) = x

⊦ ∀P. (∀x y. P (Data.Pair., x y)) ⇒ ∀p. P p

⊦ ∀PAIR'. ∃fn. ∀a0 a1. fn (Data.Pair., a0 a1) = PAIR' a0 a1

Input Type Operators

• →
• bool
• Data
  • Pair
    • Data.Pair.*

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • T
  • Pair
    • Data.Pair.,
    • Data.Pair.fst
    • Data.Pair.snd

Assumptions

⊦ T

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀x y. Data.Pair.fst (Data.Pair., x y) = x

⊦ ∀x y. Data.Pair.snd (Data.Pair., x y) = y

⊦ ∀p. ∃x y. p = Data.Pair., x y

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q