chainBotCoeff_of_not_linearIndependent

English

Given a bijection of supports e and equality of Cartan matrices under e, the constructed equivOfCartanMatrixEq yields an equivalence of root pairings P and P2.

Русский

При биекции опор e и равенстве Картановых матриц, построенный эквив по Картану задаёт эквивалентность корневых пар P и P2.

LaTeX

$$Equiv (RootPairing) between P and P2 induced by Cartan data$$

Lean4

theorem chainBotCoeff_of_not_linearIndependent (h : ¬LinearIndependent R ![P.root i, P.root j]) :
    P.chainBotCoeff i j = 0 := by simp only [chainBotCoeff, h, reduceDIte]

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