Package natural-numeral: Definitions and theorems about natural number numerals

Information

Files

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

Defined Constants

• Number
  • Numeral
    • bit0
    • bit1

Theorems

⊦ 1 = suc 0

⊦ 2 = suc 1

⊦ ∀n. bit1 n = suc (bit0 n)

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

Input Type Operators

• →
• bool
• Number
  • Natural
    • natural

Input Constants

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

Assumptions

⊦ T

⊦ (∃) = λP. P ((select) P)

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ ∀e f. ∃fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n