rootForm_restrict_nondegenerate_of_isAnisotropic

English

The restriction of RootForm to the root span is nondegenerate.

Русский

Ограничение корневой формы на корневойSPAN не вырождено.

LaTeX

$$Раздел RootForm на rootSpan R: Nondegenerate$$

Lean4

/-- See also `RootPairing.rootForm_restrict_nondegenerate_of_ordered`.

Note that this applies to crystallographic root systems in characteristic zero via
`RootPairing.instIsAnisotropicOfIsCrystallographic`. -/
theorem rootForm_restrict_nondegenerate_of_isAnisotropic :
    LinearMap.Nondegenerate (P.RootForm.restrict (P.rootSpan R)) :=
  P.rootForm_symmetric.nondegenerate_restrict_of_isCompl_ker P.isCompl_rootSpan_ker_rootForm

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