Theorems · Theorem · order theory
Set.insert_subset_iff
∀ {α : Type u_1} {s t : Set α} {a : α}, insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by35
Results whose statement or proof uses this declaration.
- Submodule.span_insert_zeroproof · cited by 11
- affineSpan_pair_le_of_mem_of_memproof · cited by 6
- Submodule.span_insert_eq_spanproof · cited by 5
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Matroid.Indep.mem_closure_iff'proof · cited by 5
- Set.ordConnected_of_Iooproof · cited by 4
- Set.wcovBy_insertproof · cited by 4
- Matroid.Indep.notMem_closure_iffproof · cited by 3
- Vitali.exists_disjoint_subfamily_covering_enlargementproof · cited by 3
- MeasureTheory.IsSetSemiring.isSetRing_supClosureproof · cited by 3
- Matroid.IsBase.exchange_isBase_of_indepproof · cited by 3
- Matroid.Indep.insert_indep_iff_of_notMemproof · cited by 3