Theorems · Theorem · combinatorics
Finset.mem_of_mem_insert_of_ne
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} {a b : α}, b ∈ insert a s → b ≠ a → b ∈ s- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 55 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.mem_insertproof · cited by 44
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCofiltered.inf_objs_existsproof · cited by 7
- MonovaryOn.sum_smul_comp_perm_le_sum_smulproof · cited by 7
- CategoryTheory.IsCofiltered.inf_existsproof · cited by 6
- CategoryTheory.IsFiltered.sup_existsproof · cited by 5
- CategoryTheory.IsFiltered.sup_objs_existsproof · cited by 2
- Nat.factoredNumbers_insertproof · cited by 2
- Finset.prodPiInsertproof · cited by 1
- Finset.Colex.shadow_initSegproof · cited by 1
- Finset.inf_supproof · cited by 1