Theorems · Theorem · nonassociative algebras

RootPairing.Base.pairingIn_le_zero_of_ne

∀ {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} (b : P.Base)
  [CharZero R] [IsDomain R] [inst_7 : P.IsCrystallographic] [Finite ι] {i j : ι},
  i ≠ j → i ∈ b.support → j ∈ b.support → P.pairingIn ℤ i j ≤ 0

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

2 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCharZeroIsDomainRootPairing.IsCrystallographicFinite