Theorems · Theorem · order theory
Set.preimage_inter
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s t : Set β}, f ⁻¹' (s ∩ t) = f ⁻¹' s ∩ f ⁻¹' t- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 6 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 by25
Results whose statement or proof uses this declaration.
- Set.inter_invproof · cited by 11
- Set.inter_negproof · cited by 11
- IsPiSystem.comapproof · cited by 3
- LocallyBoundedVariationOn.ofDualproof · cited by 2
- ContinuousOn.preimage_mem_nhdsSetWithinproof · cited by 2
- IsSemilinearSet.interproof · cited by 2
- Disjoint.of_preimageproof · cited by 2
- IsOpen.exists_contMDiff_support_eqproof · cited by 1
- BoundedVariationOn.tendsto_eVariationOn_Icc_zero_rightproof · cited by 1
- IsClosed.mem_of_ge_of_forall_exists_ltproof · cited by 1
- LocallyBoundedVariationOn.tendsto_eVariationOn_Icc_rightproof · cited by 1