Theorems · Theorem · order theory
Set.image_prod
∀ {α : Type u_1} {β : Type u_3} {γ : Type u_5} (f : α → β → γ) {s : Set α} {t : Set β},
(fun x => f x.1 x.2) '' s ×ˢ t = Set.image2 f s t- Defined in
- Mathlib.Data.Set.NAry
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.extproof · cited by 2,266
- SProd.sprodstatement and proof · cited by 1,750
- Set.image2statement · cited by 311
Cited by24
Results whose statement or proof uses this declaration.
- Finset.subset_set_image₂proof · cited by 10
- Set.add_image_prodproof · cited by 8
- Set.image_mul_prodproof · cited by 4
- Set.image_uncurry_prodproof · cited by 4
- AffineSubspace.isConnected_setOfPred_sSameSideproof · cited by 3
- sSup_image2proof · cited by 3
- Set.vadd_image_prodproof · cited by 2
- MeasureTheory.Measure.toSphere_apply_auxproof · cited by 2
- Set.image_smul_prodproof · cited by 2
- AffineSubspace.isConnected_setOfPred_sOppSideproof · cited by 2
- AffineSubspace.isConnected_setOfPred_wOppSideproof · cited by 2
- AffineSubspace.isConnected_setOfPred_wSameSideproof · cited by 2