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import Adam.Metadata
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import Mathlib.Algebra.Module.Submodule.Lattice
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Game "Adam"
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World "Module"
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Level 5
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Title "Untervektorräume"
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Introduction
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"
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Elemente aus einem Untervektorraum $U$ wählt man gleich aus, wie Elemente in einer Menge.
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Nämlich man nimmt ein Element `(x : V)` und sagt, dass es in `U` liegt mit `x ∈ U` (`\\in`).
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"
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Statement
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"TODO: Spannendere Aufgaben."
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{K V : Type _} [Field K] [AddCommMonoid V] [Module K V] (U : Submodule K V) :
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∀ (x : V), x ∈ U ∨ x ∉ U := by
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intro x
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rw [or_iff_not_imp_left]
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tauto
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