Theorems · Theorem · nonassociative algebras

RootPairing.Base.IsPos.exists_mem_support_pos_pairingIn

∀ {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}
  [inst_5 : CharZero R] [inst_6 : P.IsCrystallographic] {i : ι}, b.IsPos i → ∃ j ∈ b.support, 0 < P.pairingIn ℤ j i

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

3 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCharZeroRootPairing.IsCrystallographic