Package natural-add-numeral: natural-add-numeral
Information
| name | natural-add-numeral |
| version | 1.3 |
| description | natural-add-numeral |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| show | Data.Bool |
Files
- Package tarball natural-add-numeral-1.3.tgz
- Theory file natural-add-numeral.thy (included in the package tarball)
Theorems
⊦ ∀n. Number.Natural.bit0 n = Number.Natural.+ n n
⊦ ∀n. Number.Natural.bit1 n = Number.Natural.suc (Number.Natural.+ n n)
Input Type Operators
- →
- bool
- Number
- Natural
- Number.Natural.natural
- Natural
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- T
- Bool
- Number
- Natural
- Number.Natural.+
- Number.Natural.bit0
- Number.Natural.bit1
- Number.Natural.suc
- Number.Natural.zero
- Natural
Assumptions
⊦ T
⊦ ∀t. (∀x. t) ⇔ 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))
⊦ ∀P. P 0 ∧ (∀n. P n ⇒ P (Number.Natural.suc n)) ⇒ ∀n. P n
⊦ (∀n. Number.Natural.+ 0 n = n) ∧ (∀m. Number.Natural.+ m 0 = m) ∧
(∀m n.
Number.Natural.+ (Number.Natural.suc m) n =
Number.Natural.suc (Number.Natural.+ m n)) ∧
∀m n.
Number.Natural.+ m (Number.Natural.suc n) =
Number.Natural.suc (Number.Natural.+ m n)