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Update Mathlib/Topology/Algebra/Module/ModuleTopology.lean
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Co-authored-by: Oliver Nash <[email protected]>
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kbuzzard and ocfnash authored Jan 12, 2025
1 parent 7133502 commit c99e6bc
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions Mathlib/Topology/Algebra/Module/ModuleTopology.lean
Original file line number Diff line number Diff line change
Expand Up @@ -433,9 +433,9 @@ instance instProd : IsModuleTopology R (M × N) := by
refine le_antisymm ?_ <| sInf_le ⟨Prod.continuousSMul, Prod.continuousAdd⟩
-- Or equivalently, if `P` denotes `M × N` with the module topology,
let P := M × N
letI τP : TopologicalSpace P := moduleTopology R P
haveI : IsModuleTopology R P := ⟨rfl⟩
haveI : ContinuousAdd P := ModuleTopology.continuousAdd R P
let τP : TopologicalSpace P := moduleTopology R P
have : IsModuleTopology R P := ⟨rfl⟩
have : ContinuousAdd P := ModuleTopology.continuousAdd R P
-- and if `i` denotes the identity map from `M × N` to `P`
let i : M × N → P := id
-- then we need to show that `i` is continuous.
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