Theorems · Theorem · nonassociative algebras

RootPairing.finrank_rootSpanIn

∀ {ι : Type u_1} {M : Type u_4} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] (K : Type u_7)
  {L : Type u_8} [inst_2 : Field K] [inst_3 : Field L] [inst_4 : Algebra K L] [inst_5 : Module L M]
  [inst_6 : Module L N] [inst_7 : Module K M] [inst_8 : Module K N] [IsScalarTower K L M] [IsScalarTower K L N]
  (Q : RootPairing ι L M N) [Q.IsRootSystem] [Q.IsValuedIn K], Module.finrank K ↥(Q.rootSpan K) = Module.finrank L M

Defined in

Mathlib.LinearAlgebra.RootSystem.IsValuedIn

Cited by

3 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupFieldFieldAlgebraModuleModuleModuleModuleIsScalarTowerIsScalarTowerRootPairing.IsRootSystemRootPairing.IsValuedIn