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Theorems · Theorem · functional analysis

Submodule.closure.congr_simp

∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : TopologicalSpace M]
  [inst_3 : Module R M] [inst_4 : ContinuousAdd M] [inst_5 : ContinuousConstSMul R M] (s s_1 : Submodule R M),
  s = s_1 → s.closure = s_1.closure
Defined in
Mathlib.Topology.Algebra.Module.ClosedSubmodule
Cited by
1 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringAddCommMonoidTopologicalSpaceModuleContinuousAddContinuousConstSMul
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Around this declaration

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

ClosedSubmodule.map_id · cited by 1ClosedSubmodule.map_idTopologicalSpace · cited by 24529TopologicalSpaceModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidSubmodule · cited by 7192SubmoduleContinuousConstSMul · cited by 832ContinuousConstSMulContinuousAdd · cited by 777ContinuousAddClosedSubmodule · cited by 123ClosedSubmoduleSubmodule.closure · cited by 16Submodule.closureclosure.congr_simpCITED BYCITES

Cites9

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Cited by1

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