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Theorems · Theorem · order theory

Set.preimage_sUnion

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set (Set β)}, f ⁻¹' ⋃₀ s = ⋃ t ∈ s, f ⁻¹' t
Defined in
Mathlib.Data.Set.Lattice.Image
Cited by
2 results in Mathlib
Foundations
Depth 62 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.sUnion_neg · cited by 0Set.sUnion_negSet.sUnion_inv · cited by 0Set.sUnion_invSet · cited by 53352SetSet.preimage · cited by 4946Set.preimageSet.iUnion · cited by 2483Set.iUnionSet.sUnion · cited by 392Set.sUnionSet.sUnion_eq_biUnion · cited by 51Set.sUnion_eq_biUnionSet.preimage_iUnion₂ · cited by 6Set.preimage_iUnion₂Set.preimage_sUnionCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.