Package natural-add-sub-def: Definition of natural number subtraction
Information
| name | natural-add-sub-def |
| version | 1.5 |
| description | Definition of natural number subtraction |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-01-13 |
| requires | bool natural-add-thm natural-def natural-dest natural-thm |
| show | Data.Bool Number.Natural |
Files
- Package tarball natural-add-sub-def-1.5.tgz
- Theory source file natural-add-sub-def.thy (included in the package tarball)
Defined Constant
- Number
- Natural
- -
- Natural
Theorem
⊦ ∀m n. m + n - n = m
External Type Operators
- →
- bool
- Number
- Natural
- natural
- Natural
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ⊤
- Bool
- Number
- Natural
- +
- pre
- suc
- zero
- Natural
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀n. pre (suc n) = n
⊦ ∀m. m + 0 = m
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀m n. m + suc n = suc (m + n)
⊦ ∀r. (∀x. ∃y. r x y) ⇔ ∃f. ∀x. r x (f x)
⊦ ∀p. p 0 ∧ (∀n. p n ⇒ p (suc n)) ⇒ ∀n. p n
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n