Package set-finite-def: Definition of finite sets
Information
| name | set-finite-def |
| version | 1.24 |
| description | Definition of finite sets |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2012-06-16 |
| requires | bool |
| show | Data.Bool Set |
Files
- Package tarball set-finite-def-1.24.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
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- ⊤
- Bool
- Set
- ∅
- insert
Assumptions
⊦ ⊤
⊦ (∀) = λp. p = λx. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = 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
⊦ ∀p1 p2 q1 q2. (p1 ⇒ p2) ∧ (q1 ⇒ q2) ⇒ p1 ∧ q1 ⇒ p2 ∧ q2
⊦ ∀p1 p2 q1 q2. (p1 ⇒ p2) ∧ (q1 ⇒ q2) ⇒ p1 ∨ q1 ⇒ p2 ∨ q2