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.
Cites5
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.Subset.antisymmproof · cited by 213
- Set.sdiff_subsetproof · cited by 156
- Set.union_subsetproof · cited by 71
- Set.subset_sdiff_unionproof · cited by 6
Cited by18
Results whose statement or proof uses this declaration.
- Set.encard_sdiff_add_encard_of_subsetproof · cited by 6
- MeasureTheory.measure_eq_measure_of_between_null_sdiffproof · cited by 4
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
- MeasureTheory.setIntegral_sdiff₀proof · cited by 3
- Matroid.IsBasis.contract_eq_contract_deleteproof · cited by 3
- MeasureTheory.SignedMeasure.exists_compl_positive_negativeproof · cited by 2
- MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closedproof · cited by 2
- Set.Finite.ecard_lt_ecardproof · cited by 2
- closure_sUnion_irreducibleComponents_sdiff_singletonproof · cited by 2
- MeasureTheory.SignedMeasure.bddBelow_measureOfNegativesproof · cited by 1
- SeparatedNhds.of_isClosed_isCompact_closure_compl_isClosedproof · cited by 1
- Cardinal.mk_sdiff_add_mkproof · cited by 1