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Theorems · Theorem · order theory

Set.image_swap_prod

∀ {α : Type u_1} {β : Type u_2} (s : Set α) (t : Set β), Prod.swap '' s ×ˢ t = t ×ˢ s
Defined in
Mathlib.Data.Set.Prod
Cited by
5 results in Mathlib
Foundations
Depth 17 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.

Finset.image_swap_product · cited by 2Finset.image_swap_productSet.prod_image_seq_comm · cited by 1Set.prod_image_seq_commFinset.map_swap_product · cited by 1Finset.map_swap_productSetRel.prod_subset_comm · cited by 0SetRel.prod_subset_commPointedCone.IsFaceOf.snd · cited by 0IsFaceOf.sndSet · cited by 53352SetSet.image · cited by 5609Set.imageSProd.sprod · cited by 1750SProd.sprodSet.preimage_swap_prod · cited by 5Set.preimage_swap_prodSet.image_swap_eq_preimage_swap · cited by 4Set.image_swap_eq_preimag…Set.image_swap_prodCITED BYCITES

Cites5

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

Cited by5

Results whose statement or proof uses this declaration.