Theorems · Theorem · nonassociative algebras

RootPairing.finrank_corootSpanIn_int

∀ {ι : Type u_1} {M : Type u_4} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] {L : Type u_8}
  [inst_2 : Field L] [inst_3 : Module L M] [inst_4 : Module L N] (Q : RootPairing ι L M N) [Q.IsRootSystem] [Finite ι]
  [CharZero L] [Q.IsCrystallographic], Module.finrank ℤ ↥(Q.corootSpan ℤ) = Module.finrank L N

Defined in

Mathlib.LinearAlgebra.RootSystem.IsValuedIn

Cited by

0 results in Mathlib

Foundations

Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupFieldModuleModuleRootPairing.IsRootSystemFiniteCharZeroRootPairing.IsCrystallographic