Theorems · Theorem · order theory
Set.preimage_comp
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {f : α → β} {g : β → γ} {s : Set γ}, g ∘ f ⁻¹' s = f ⁻¹' g ⁻¹' s- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.preimagestatement · cited by 4,946
Cited by57
Results whose statement or proof uses this declaration.
- Set.preimage_preimageproof · cited by 36
- AEMeasurable.map_map_of_aemeasurableproof · cited by 28
- ProbabilityTheory.Kernel.IndepFun.compproof · cited by 26
- continuousOn_iff'proof · cited by 9
- Function.LeftInverse.preimage_preimageproof · cited by 5
- OpenPartialHomeomorph.extend_image_target_mem_nhdsproof · cited by 4
- MeasureTheory.Measure.QuasiMeasurePreserving.preimage_iterate_ae_eqproof · cited by 4
- Cardinal.infinite_pigeonhole_cardproof · cited by 4
- isInducing_stoneCechUnitproof · cited by 4
- IsLocallyConstant.compproof · cited by 4
- EReal.preimage_coe_Ioiproof · cited by 3
- EReal.preimage_coe_Ioi_botproof · cited by 3