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Theorems · Theorem · order theory

Set.sInter_subset_sInter

∀ {α : Type u_1} {S T : Set (Set α)}, S ⊆ T → ⋂₀ T ⊆ ⋂₀ S
Defined in
Mathlib.Data.Set.Lattice
Cited by
5 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.sInter_mono · cited by 3Set.sInter_monoFilter.mem_countableGenerate_iff · cited by 1Filter.mem_countableGener…Matroid.fundCircuit_restrict · cited by 0Matroid.fundCircuit_restr…Filter.mem_cardinalGenerate_iff · cited by 0Filter.mem_cardinalGenera…Filter.nhds_mono · cited by 0Filter.nhds_monoSet · cited by 53352SetSet.sInter · cited by 225Set.sInterSet.sInter_subset_of_mem · cited by 28Set.sInter_subset_of_memSet.subset_sInter · cited by 8Set.subset_sInterSet.sInter_subset_sInterCITED BYCITES

Cites4

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Cited by5

Results whose statement or proof uses this declaration.