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import Adam.Metadata
import Mathlib.Algebra.Module.Submodule.Lattice
import Mathlib.Data.Real.Basic
import Mathlib.LinearAlgebra.Basic
Game "Adam"
World "Module2"
Level 3
Title "Lineare Abbildung"
Introduction
"
"
Statement
""
{R V : Type _} [Semiring R] [AddCommGroup V] [Module R V]
(p : V →ₗ[R] V) (h : p ∘ p = p) : LinearMap.ker p ⊔ LinearMap.range p = ⊤ := by
sorry
-- rw eq_top_iff,
-- intros v hv,
-- rw ←sub_add_cancel v (p v),
-- apply submodule.add_mem_sup,
-- { rw [linear_map.mem_ker],
-- rw [map_sub],
-- change p v - (p ∘ p) v = 0, -- oder: rw [function.comp, function.funext_iff] at h,