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import Adam.Metadata
import Mathlib.Algebra.Module.Submodule.Lattice
import Mathlib.LinearAlgebra.Span
open Submodule
Game "Adam"
World "Module2"
Level 5
Title "Lineare Abbildung"
Introduction
"
Die interne Summe von Untermodulen wird in Lean mit `⊔` (`\\sup`) geschrieben.
"
Statement
"
Zeige, dass `V₁ ⊔ V₂` tatsächlich die interne Summe `⟨V₁ ∪ V₂⟩` ist.
"
{K V : Type _} [Field K] [AddCommMonoid V] [Module K V] (V₁ V₂ : Submodule K V) :