Theorems · Theorem · nonassociative algebras

RootPairing.IsIrreducible.nontrivial

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} {inst : CommRing R} {inst_1 : AddCommGroup M}
  {inst_2 : Module R M} {inst_3 : AddCommGroup N} {inst_4 : Module R N} (P : RootPairing ι R M N)
  [self : P.IsIrreducible], Nontrivial M

Defined in

Mathlib.LinearAlgebra.RootSystem.Irreducible

Cited by

2 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

RootPairing.IsIrreducible