Package natural-even-odd-def: natural-even-odd-def

Information

Files

• Package tarball natural-even-odd-def-1.0.tgz
• Theory file natural-even-odd-def.thy (included in the package tarball)

Defined Constants

• Number
  • Natural
    • Number.Natural.even
    • Number.Natural.odd

Theorems

⊦ (Number.Natural.even Number.Numeral.zero ⇔ T) ∧
  ∀n. Number.Natural.even (Number.Natural.suc n) ⇔ ¬Number.Natural.even n

⊦ (Number.Natural.odd Number.Numeral.zero ⇔ F) ∧
  ∀n. Number.Natural.odd (Number.Natural.suc n) ⇔ ¬Number.Natural.odd n

Input Type Operators

• →
• bool
• Number
  • Natural
    • Number.Natural.natural

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ¬
    • select
    • F
    • T
• Number
  • Natural
    • Number.Natural.suc
  • Numeral
    • Number.Numeral.zero

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

⊦ ∀e f.
    ∃fn.
      fn Number.Numeral.zero = e ∧
      ∀n. fn (Number.Natural.suc n) = f (fn n) n