Theorems · Theorem · combinatorics
Finset.card_insert_of_notMem
∀ {α : Type u_1} {s : Finset α} {a : α} [inst : DecidableEq α], a ∉ s → (insert a s).card = s.card + 1- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- Finset.cardstatement · cited by 2,327
Cited by45
Results whose statement or proof uses this declaration.
- Finset.card_eq_succproof · cited by 7
- Nat.count_nthproof · cited by 5
- SimpleGraph.IsNClique.insertproof · cited by 3
- Finpartition.equitabilise_auxproof · cited by 3
- SimpleGraph.is3Clique_triple_iffproof · cited by 2
- Dynamics.coverMincard_le_netMaxcardproof · cited by 2
- SimpleGraph.IsFiveWheelLike.card_leftproof · cited by 2
- Polynomial.card_support_binomialproof · cited by 2
- Sym2.card_toFinset_of_not_isDiagproof · cited by 2
- Polynomial.card_support_trinomialproof · cited by 2
- Equiv.Perm.isThreeCycle_swap_mul_swap_sameproof · cited by 2
- Submodule.iUnion_ssubset_of_forall_ne_top_of_card_ltproof · cited by 1