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import Adam.Metadata
import Mathlib.Algebra.Module.Submodule.Lattice
import Mathlib.Data.Real.Basic -- definiert `ℝ
import Mathlib.Algebra.Module.LinearMap -- definiert `→ₗ`
import Mathlib.Tactic.FinCases
import Mathlib.Data.Fin.VecNotation
-- import Mathlib.LinearAlgebra.Finsupp
import Mathlib.Algebra.BigOperators.Basic -- default
-- import Mathlib.LinearAlgebra.LinearIndependent
import Mathlib
Game "Adam"
World "Basis"
Level 2
Title "Lineare Unabhängigkeit"
namespace Ex_LinIndep
scoped notation "ℝ²" => Fin 2 → ℝ
Introduction
"
"
Statement
"Zeige, dass `![1, 0], ![1, 1]` linear unabhängig über `ℝ
: LinearIndependent ℝ
Hint "`rw [Fintype.linearIndependent_iff]`"
rw [Fintype.linearIndependent_iff]
Hint "`intros c h`"
intros c h
Hint "BUG: `simp at h` does not work :("
simp at h -- doesn't work
sorry
-- rw [Fintype.linearIndependent_iff]
-- intros c h
-- simp at h
-- intros i
-- fin_cases i
-- swap
-- { exact h.2 }
-- { have h' := h.1
-- rw [h.2, add_zero] at h'
-- exact h'}
end Ex_LinIndep