Package natural-pre: natural-pre

Information

Files

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

Defined Constant

• Number
  • Natural
    • Number.Natural.pre

Theorems

⊦ Number.Natural.pre Number.Numeral.zero = Number.Numeral.zero

⊦ ∀n. Number.Natural.pre (Number.Natural.suc n) = n

Input Type Operators

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

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • select
    • 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