rootSpace_two_smul — Mathlib

English

The chainTopCoeff after modifying β by adding nα shifts by the same n, i.e., chainTopCoeff α β' = chainTopCoeff α β − n.

Русский

При добавлении nα к β коэффициент chainTopCoeff смещается на −n: chainTopCoeff α β' = chainTopCoeff α β − n.

LaTeX

$$$\operatorname{chainTopCoeff}(α, β') = \operatorname{chainTopCoeff}(α, β) - n$$$

Lean4

theorem rootSpace_two_smul (hα : α.IsNonZero) : rootSpace H (2 • α) = ⊥ :=
  by
  cases subsingleton_or_nontrivial L
  · exact IsEmpty.elim inferInstance α
  simpa [chainTopCoeff_zero_right α hα] using genWeightSpace_chainTopCoeff_add_one_nsmul_add α (0 : Weight K H L) hα

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