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more tidying up
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FLT/ForMathlib/module_topology.lean

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@@ -520,8 +520,6 @@ def Module.topologicalRing : TopologicalRing D :=
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end commutative
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set_option linter.unusedTactic false
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lemma continuousSMul (R : Type*) [CommRing R] [TopologicalSpace R] [TopologicalRing R]
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(A : Type*) [AddCommGroup A] [Module R A] [Module.Finite R A] [TopologicalSpace A]
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[IsModuleTopology R A] :
@@ -536,8 +534,7 @@ end ModuleTopology
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I can only prove that `SMul : R × A → A` is continuous for the module topology if `R` is
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commutative (because my proof uses tensor products) and if `A` is finite (because
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I reduce to a basis check ). Is it true in general
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I reduce to a basis check ). Is it true in general?
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lemma continuousSMul (R : Type*) [Ring R] [TopologicalSpace R] [TopologicalRing R]
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(A : Type*) [AddCommGroup A] [Module R A] : @ContinuousSMul R A _ _ (moduleTopology R A) := by
@@ -546,6 +543,4 @@ lemma continuousSMul (R : Type*) [Ring R] [TopologicalSpace R] [TopologicalRing
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rw [isModuleTopology R R]
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refine Module.continuous_bilinear ?_
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sorry
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done
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end ModuleTopology
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-/

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