Theorems · Theorem · nonassociative algebras

RootPairing.IsAnisotropic.rootForm_root_ne_zero

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} {inst : Fintype ι} {inst_1 : AddCommGroup M}
  {inst_2 : AddCommGroup N} {inst_3 : CommRing R} {inst_4 : Module R M} {inst_5 : Module R N} {P : RootPairing ι R M N}
  [self : P.IsAnisotropic] (i : ι), (P.RootForm (P.root i)) (P.root i) ≠ 0

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate

Cited by

3 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Quot.sound

Assumes

RootPairing.IsAnisotropic