Package natural-numeral-thm: natural-numeral-thm

Information

Files

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

Theorems

⊦ 1 = Number.Natural.suc 0

⊦ 2 = Number.Natural.suc 1

Input Type Operators

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

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • T
• Number
  • Natural
    • Number.Natural.bit0
    • Number.Natural.bit1
    • Number.Natural.suc
    • Number.Natural.zero

Assumptions

⊦ T

⊦ (∀) = λp. p = λx. T

⊦ ∀x. x = x ⇔ T

⊦ ∀n. Number.Natural.bit1 n = Number.Natural.suc (Number.Natural.bit0 n)

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ Number.Natural.bit0 0 = 0 ∧
  ∀n.
    Number.Natural.bit0 (Number.Natural.suc n) =
    Number.Natural.suc (Number.Natural.suc (Number.Natural.bit0 n))