Theorems · Theorem · order theory
Set.subset_sdiff_singleton
∀ {α : Type u_1} {s t : Set α} {a : α}, s ⊆ t → a ∉ s → s ⊆ t \ {a}- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.singleton_subset_iffproof · cited by 206
- Set.subset_interproof · cited by 74
- Set.subset_compl_commproof · cited by 22
Cited by14
Results whose statement or proof uses this declaration.
- Matroid.Indep.exists_insert_of_not_isBaseproof · cited by 5
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
- Matroid.indep_iff_forall_notMem_closure_sdiffproof · cited by 3
- Set.minimal_iff_forall_sdiff_singletonproof · cited by 3
- Matroid.IsCircuit.isBasis_iff_eq_sdiff_singletonproof · cited by 2
- EuclideanGeometry.exists_of_range_subset_orthocentricSystemproof · cited by 2
- convexIndependent_set_iff_notMem_convexHull_sdiffproof · cited by 2
- Matroid.Indep.mem_fundCircuit_iffproof · cited by 1
- Matroid.fundCircuit_sdiff_eq_interproof · cited by 1
- Matroid.Indep.union_indep_iff_forall_notMem_closure_rightproof · cited by 1
- Set.mem_Icc_Ico_Ioc_Ioo_of_subset_of_subsetproof · cited by 1
- Set.subset_diff_singletonproof · cited by 0