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Theorems · Theorem · order theory

Set.sdiff_union_of_subset

∀ {α : Type u_1} {s t : Set α}, t ⊆ s → s \ t ∪ t = s
Defined in
Mathlib.Order.BooleanAlgebra.Set
Cited by
18 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.

Set.encard_sdiff_add_encard_of_subset · cited by 6Set.encard_sdiff_add_enca…MeasureTheory.measure_eq_measure_of_between_null_sdiff · cited by 4MeasureTheory.measure_eq_…Matroid.IsCircuit.contract_isCircuit · cited by 4IsCircuit.contract_isCirc…MeasureTheory.setIntegral_sdiff₀ · cited by 3MeasureTheory.setIntegral…Matroid.IsBasis.contract_eq_contract_delete · cited by 3IsBasis.contract_eq_contr…MeasureTheory.SignedMeasure.exists_compl_positive_negative · cited by 2SignedMeasure.exists_comp…MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closed · cited by 2MeasureTheory.exists_cont…Set.Finite.ecard_lt_ecard · cited by 2Finite.ecard_lt_ecardclosure_sUnion_irreducibleComponents_sdiff_singleton · cited by 2closure_sUnion_irreducibl…MeasureTheory.SignedMeasure.bddBelow_measureOfNegatives · cited by 1SignedMeasure.bddBelow_me…SeparatedNhds.of_isClosed_isCompact_closure_compl_isClosed · cited by 1SeparatedNhds.of_isClosed…Cardinal.mk_sdiff_add_mk · cited by 1Cardinal.mk_sdiff_add_mkMatroid.IsBasis'.contract_dep_iff · cited by 1IsBasis'.contract_dep_iffMatroid.Indep.union_isBasis_union_of_contract_isBasis · cited by 0Indep.union_isBasis_union…Set.diff_union_of_subset · cited by 0Set.diff_union_of_subsetSet · cited by 53352SetSet.Subset.antisymm · cited by 213Subset.antisymmSet.sdiff_subset · cited by 156Set.sdiff_subsetSet.union_subset · cited by 71Set.union_subsetSet.subset_sdiff_union · cited by 6Set.subset_sdiff_unionSet.sdiff_union_of_subsetCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.