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Theorems · Theorem · general topology

Filter.prod_eq

∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {g : Filter β}, f ×ˢ g = (Filter.map Prod.mk f).seq g
Defined in
Mathlib.Order.Filter.Prod
Cited by
3 results in Mathlib
Foundations
Depth 63 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.

Filter.prod_pure · cited by 30Filter.prod_pureFilter.pure_prod · cited by 10Filter.pure_prodList.tendsto_cons_iff · cited by 1List.tendsto_cons_iffFilter · cited by 8121FilterSProd.sprod · cited by 1750SProd.sprodFilter.map · cited by 819Filter.mapFilter.seq · cited by 15Filter.seqFilter.map_prod · cited by 2Filter.map_prodFilter.prod_eqCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.