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import TestGame.Metadata
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import Mathlib.Algebra.Module.Submodule.Lattice
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import Mathlib.LinearAlgebra.Span
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open Submodule
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Game "TestGame"
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World "Module2"
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Level 6
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Title "Lineare Abbildung"
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Introduction
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"
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Eine interne Summe über eine Familie von Untermodulen `(T : ι → submodule K V)`
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wird als `⨆ (i : ι), T i` geschrieben (`\\supr`).
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"
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Statement
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""
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{K V ι : Type _} [Field K] [AddCommMonoid V] [Module K V]
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(T : ι → Submodule K V) : (⨆ (i : ι), T i) = span K ( ⋃ i, T i) := by
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rw [Submodule.span_unionᵢ]
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simp
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