Theorems · Definition · combinatorics
Fintype.subtype
{α : Type u_1} → {p : α → Prop} → (s : Finset α) → (∀ (x : α), x ∈ s ↔ p x) → Fintype { x // p x }Given a predicate that can be represented by a finset, the subtype associated to the predicate is a fintype.
- Defined in
- Mathlib.Data.Fintype.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Fintypestatement · cited by 7,736
- Finset.valproof · cited by 438
- Multiset.pmapproof · cited by 16
Cited by6
Results whose statement or proof uses this declaration.
- Fintype.card_of_subtypeproof · cited by 9
- Fintype.subtype_cardstatement · cited by 7
- Fintype.ofFinsetproof · cited by 4
- Subfield.fintypeBotproof · cited by 2
- Nat.CountSet.fintypeproof · cited by 1
- UniqueFactorizationMonoid.fintypeSubtypeDvdproof · cited by 1