Theorems · Theorem · nonassociative algebras

RootPairing.IsIrreducible.eq_top_of_invtSubmodule_coreflection

∀ {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] (q : Submodule R N),
  (∀ (i : ι), q ∈ Module.End.invtSubmodule ↑(P.coreflection i)) → q ≠ ⊥ → q = ⊤

Defined in

Mathlib.LinearAlgebra.RootSystem.Irreducible

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RootPairing.IsIrreducible