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34 lines
644 B
Plaintext
34 lines
644 B
Plaintext
2 years ago
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import TestGame.Metadata
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import Mathlib.Algebra.Module.Submodule.Lattice
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import Mathlib.Data.Real.Basic
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import Mathlib.LinearAlgebra.Basic
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Game "TestGame"
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World "Module2"
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Level 4
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Title "Lineare Abbildung"
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Introduction
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"
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"
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Statement
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""
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{R V : Type _} [Semiring R] [AddCommGroup V] [Module R V]
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(p : V →ₗ[R] V)(h : p ∘ p = p) : LinearMap.ker p ⊓ LinearMap.range p = ⊥ := by
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sorry
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-- rw eq_bot_iff,
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-- intros v hv,
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-- rw submodule.mem_bot,
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-- rw submodule.mem_inf at hv,
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-- cases hv.2 with w hw,
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-- rw ←hw,
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-- rw ←h,
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-- change p (p w) = _,
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-- rw hw,
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-- rw ←linear_map.mem_ker,
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-- exact hv.1,
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