Theorems · Theorem · combinatorics
Finset.cons_eq_insert
∀ {α : Type u_1} [inst : DecidableEq α] (a : α) (s : Finset α) (h : a ∉ s), Finset.cons a s h = insert a s- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 58 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.
Cites3
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.extproof · cited by 565
- Finset.consstatement · cited by 221
Cited by59
Results whose statement or proof uses this declaration.
- Finset.inductionproof · cited by 108
- Nat.cons_self_properDivisorsproof · cited by 11
- Finset.noncommProd_insert_of_notMemproof · cited by 8
- Finset.Icc_eq_cons_Icoproof · cited by 7
- Finset.Icc_eq_cons_Iocproof · cited by 6
- Finset.Iic_eq_cons_Iioproof · cited by 5
- Finset.Ico_eq_cons_Iooproof · cited by 4
- Nat.multinomial_insertproof · cited by 4
- Fin.univ_succproof · cited by 3
- StrictConvexOn.map_sum_ltproof · cited by 3
- Finset.noncommSum_insert_of_notMemproof · cited by 3
- linearIndepOn_isGroupLikeElemproof · cited by 3