Mathlib Map

Theorems · Theorem · general topology

Bornology.IsBounded.fst_of_prod

∀ {α : Type u_1} {β : Type u_2} [inst : Bornology α] [inst_1 : Bornology β] {s : Set α} {t : Set β},
  Bornology.IsBounded (s ×ˢ t) → t.Nonempty → Bornology.IsBounded s
Defined in
Mathlib.Topology.Bornology.Constructions
Cited by
1 results in Mathlib
Foundations
Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
BornologyBornology
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Bornology.isBounded_prod_of_nonempty · cited by 2Bornology.isBounded_prod_…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySProd.sprod · cited by 1750SProd.sprodBornology.IsBounded · cited by 293Bornology.IsBoundedBornology · cited by 188BornologySet.fst_image_prod · cited by 8Set.fst_image_prodBornology.IsBounded.image_fst · cited by 1IsBounded.image_fstIsBounded.fst_of_prodCITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.