Theorems · Theorem · combinatorics
Finset.ssubset_insert
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α} {a : α}, a ∉ s → s ⊂ insert a s- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 59 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.Subset.rflproof · cited by 41
- Finset.ssubset_iffproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Finset.ruzsa_covering_addproof · cited by 2
- Finset.ruzsa_covering_mulproof · cited by 2
- Finset.covBy_insertproof · cited by 1
- Finset.case_strong_induction_onproof · cited by 0
- Finset.exists_subset_addSpan_card_le_of_forall_addDissociatedproof · cited by 0
- Finset.exists_subset_mulSpan_card_le_of_forall_mulDissociatedproof · cited by 0