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Theorems · Theorem · order theory

Set.image_mono

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s t : Set α}, s ⊆ t → f '' s ⊆ f '' t
Defined in
Mathlib.Data.Set.Image
Cited by
197 results in Mathlib
Foundations
Depth 16 from the axioms, rests on 79 definitions · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Submodule.map_span · cited by 84Submodule.map_spanSet.image_subset_range · cited by 76Set.image_subset_rangeIdeal.map_mono · cited by 29Ideal.map_monofinsum_eq_sum_of_support_subset · cited by 28finsum_eq_sum_of_support_…AlgebraicGeometry.Scheme.Hom.image_mono · cited by 24Hom.image_monofinprod_eq_prod_of_mulSupport_subset · cited by 21finprod_eq_prod_of_mulSup…nhdsSet_mono · cited by 18nhdsSet_monoMeasurableEmbedding.map_apply · cited by 16MeasurableEmbedding.map_a…Set.prod_subset_prod_iff · cited by 15Set.prod_subset_prod_iffSet.smul_set_mono · cited by 15Set.smul_set_monoSet.SurjOn.mono · cited by 13SurjOn.monoSubmodule.map_mono · cited by 13Submodule.map_monoIsOpenMap.image_mem_nhds · cited by 10IsOpenMap.image_mem_nhdsSet.monotone_image · cited by 9Set.monotone_imageSubgroup.map_mono · cited by 8Subgroup.map_monoSet · cited by 53352SetSet.image · cited by 5609Set.imageSet.image_monoCITED BYCITES

Cites2

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.imagestatement · cited by 5,609

Cited by197

Results whose statement or proof uses this declaration.