Mathlib Map

Theorems · Theorem · order theory

Set.card_fintypeInsertOfNotMem

∀ {α : Type u} {a : α} (s : Set α) [inst : Fintype ↑s] (h : a ∉ s), Fintype.card ↑(insert a s) = Fintype.card ↑s + 1
Defined in
Mathlib.Data.Set.Finite.Basic
Cited by
1 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Fintype
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.card_insert · cited by 0Set.card_insertSet · cited by 53352SetFintype · cited by 7736FintypeSet.Elem · cited by 7166Set.ElemFintype.card · cited by 1386Fintype.cardFinset.val · cited by 438Finset.valMultiset.cons · cited by 313Multiset.consSet.toFinset · cited by 217Set.toFinsetSet.toFinset_card · cited by 63Set.toFinset_cardFintype.card_ofFinset · cited by 26Fintype.card_ofFinsetFinset.card_cons · cited by 16Finset.card_consMultiset.nodup_cons · cited by 10Multiset.nodup_consSet.fintypeInsertOfNotMem · cited by 1Set.fintypeInsertOfNotMemSet.card_fintypeInsertOfNotMemCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.