Commit 2025-07-28 02:18 307188a2
View on Github →feat: ⋃ x ∈ s ×ˢ t, f x.1 ×ˢ g x.2 = (⋃ x ∈ s, f x) ×ˢ (⋃ x ∈ t, g x) etc. (#27016)
This lemma is needed to prove that finite product of Alexandrov-discrete spaces is Alexandrov-discrete: #27018
This is the generalization of Set.iUnion_prod to biUnion.
Also generalize pi version.
Also generalize the type of the lemma
`⋃ (i : ι), ⋃ j, ⋃ (i' : ι), ⋃ j', s i j i' j' = ⋃ (i' : ι), ⋃ j', ⋃ (i : ι), ⋃ j, s i j i' j'`
to
`⋃ (i : ι), ⋃ j, ⋃ (i' : ι'), ⋃ j', s i j i' j' = ⋃ (i' : ι'), ⋃ j', ⋃ (i : ι), ⋃ j, s i j i' j'`