Package set-finite-def: Definition of finite sets
Information
| name | set-finite-def |
| version | 1.15 |
| description | Definition of finite sets |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-11-27 |
| requires | bool |
| show | Data.Bool Set |
Files
- Package tarball set-finite-def-1.15.tgz
- Theory file set-finite-def.thy (included in the package tarball)
Defined Constants
- Set
- finite
- infinite
Theorems
⊦ finite ∅
⊦ ∀s. infinite s ⇔ ¬finite s
⊦ ∀x s. finite s ⇒ finite (insert x s)
⊦ ∀a. finite a ⇔ a = ∅ ∨ ∃x s. a = insert x s ∧ finite s
⊦ ∀FINITE'.
FINITE' ∅ ∧ (∀x s. FINITE' s ⇒ FINITE' (insert x s)) ⇒
∀a. finite a ⇒ FINITE' a
Input Type Operators
- →
- bool
- Set
- set
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- T
- Bool
- Set
- ∅
- insert
Assumptions
⊦ T
⊦ (∀) = λp. p = λx. T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀P Q. (∀x. P x ⇒ Q x) ⇒ (∃x. P x) ⇒ ∃x. Q x
⊦ ∀A B C D. (A ⇒ B) ∧ (C ⇒ D) ⇒ A ∧ C ⇒ B ∧ D
⊦ ∀A B C D. (A ⇒ B) ∧ (C ⇒ D) ⇒ A ∨ C ⇒ B ∨ D