Theorems · Theorem · logic and foundations
Set.encard_insert_of_notMem
∀ {α : Type u_1} {s : Set α} {a : α}, a ∉ s → (insert a s).encard = s.encard + 1- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- ENatstatement and proof · cited by 4,985
- Set.encardstatement and proof · cited by 327
- Set.union_singletonproof · cited by 107
- Set.encard_singletonproof · cited by 26
- Set.encard_union_eqproof · cited by 15
Cited by17
Results whose statement or proof uses this declaration.
- Set.Finite.encard_lt_topproof · cited by 10
- Set.ncard_insert_of_notMemproof · cited by 8
- Set.encard_sdiff_singleton_add_oneproof · cited by 6
- Set.encard_pairproof · cited by 3
- Set.exists_subset_encard_eqproof · cited by 3
- MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizerproof · cited by 2
- Set.encard_eq_threeproof · cited by 2
- Set.encard_eq_twoproof · cited by 2
- Set.encard_exchangeproof · cited by 2
- Metric.isCover_maximalSeparatedSetproof · cited by 1
- AddAction.isMultiplyPreprimitive_ofStabilizerproof · cited by 1
- Set.encard_eq_fourproof · cited by 1