Theorems · Definition · order theory
Set.fintypeInsertOfNotMem
{α : Type u} → {a : α} → (s : Set α) → [Fintype ↑s] → a ∉ s → Fintype ↑(insert a s)A Fintype structure on insert a s when inserting a new element.
- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Finset.valproof · cited by 438
- Multiset.consproof · cited by 313
- Set.toFinsetproof · cited by 217
- Fintype.ofFinsetproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Set.card_fintypeInsertOfNotMemstatement · cited by 1