Theorems · Theorem · nonassociative algebras

RootPairing.finrank_rootSpanIn_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.rootSpan ℤ) = Module.finrank L M

Defined in: Mathlib.LinearAlgebra.RootSystem.IsValuedIn
Cited by: 1 results in Mathlib
Foundations: Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommGroup AddCommGroup Field Module Module RootPairing.IsRootSystem Finite CharZero RootPairing.IsCrystallographic

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites21

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Fieldstatement and proof · cited by 7,404
Submodulestatement · cited by 7,192
Algebra.algebraMapproof · cited by 4,706
Set.rangeproof · cited by 4,705
Finitestatement and proof · cited by 3,029
Module.finrankstatement and proof · cited by 1,770
Submodule.spanproof · cited by 1,504
CharZerostatement and proof · cited by 932
RootPairingstatement and proof · cited by 710

Cited by1

Results whose statement or proof uses this declaration.

RootPairing.finrank_corootSpanIn_intproof · cited by 0