Theorems · Theorem · order theory
Set.insert_subset
∀ {α : Type u_1} {s t : Set α} {a : α}, a ∈ t → s ⊆ t → insert a s ⊆ t- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 16 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.
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- Matroid.Indep.closure_eq_setOfPred_isBasis_insertproof · cited by 6
- Matroid.IsBasis.mapproof · cited by 6
- Matroid.Dep.exists_isCircuit_subsetproof · cited by 5
- ZLattice.rankproof · cited by 5
- exists_linearIndepOn_extensionproof · cited by 5
- Matroid.Indep.exists_insert_of_not_isBaseproof · cited by 5
- Matroid.Indep.closure_inter_eq_self_of_subsetproof · cited by 4
- Matroid.IsBasis.insert_depproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Set.exists_subset_encard_eqproof · cited by 3
- TensorProduct.exists_finite_submodule_of_setFiniteproof · cited by 3