Theorems · Theorem · order theory
Set.iUnion_mono
∀ {α : Type u_1} {ι : Sort u_5} {s t : ι → Set α}, (∀ (i : ι), s i ⊆ t i) → ⋃ i, s i ⊆ ⋃ i, t i- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.iUnionstatement · cited by 2,483
- iSup_monoproof · cited by 37
Cited by21
Results whose statement or proof uses this declaration.
- Set.iUnion_accumulateproof · cited by 7
- exists_subset_iUnion_closed_subsetproof · cited by 4
- Set.iUnion₂_subset_iUnionproof · cited by 4
- Topology.RelCWComplex.Subcomplex.subset_complexproof · cited by 3
- ENNReal.iUnion_Iic_coe_natproof · cited by 3
- exists_subset_iUnion_ball_radius_pos_ltproof · cited by 2
- iUnion_Icc_add_zsmulproof · cited by 2
- MeasureTheory.measure_iUnion_congr_of_subsetproof · cited by 2
- setOfPred_liouville_eq_irrational_inter_iInter_iUnionproof · cited by 2
- iUnion_closure_compactCoveringproof · cited by 2
- StieltjesFunction.outer_Iocproof · cited by 2
- exists_subset_iUnion_ball_radius_ltproof · cited by 1