Package natural-dest: Natural number destructors
Information
| name | natural-dest |
| version | 1.13 |
| description | Natural number destructors |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| requires | bool natural-thm |
| show | Data.Bool Number.Natural |
Files
- Package tarball natural-dest-1.13.tgz
- Theory source file natural-dest.thy (included in the package tarball)
Defined Constant
- Number
- Natural
- pre
- Natural
Theorem
⊦ ∀n. pre (suc n) = n
External Type Operators
- →
- bool
- Number
- Natural
- natural
- Natural
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ⊤
- Bool
- Number
- Natural
- suc
- zero
- Natural
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ ∀r. (∀x. ∃y. r x y) ⇔ ∃f. ∀x. r x (f x)
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n