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import Adam.Metadata
import Adam.Options.MathlibPart
Game "Adam"
World "Module"
Level 7
Title "Hülle"
Introduction
"
"
-- notation "ℝ²" => Fin 2 → ℝ
open Submodule Set Finsupp
open BigOperators -- Summen Notation
-- TODO: Why is this not in Mathlib?
lemma mem_span_of_mem {V K : Type _} [Field K] [AddCommMonoid V]
[Module K V] (M : Set V) {x : V} (h : x ∈ M) :
x ∈ span K M := by
rw [mem_span]
intro p hp
specialize hp h
assumption
Statement
"Für $x, y \\in M$, zeige dass $x + 2y$ in der $K$-linearen Hülle $\\langle M \\rangle$ liegt."
{V K : Type _} [Field K] [AddCommMonoid V] [Module K V] (M : Set V) {x y : V}