Theorems · Theorem · nonassociative algebras

RootPairing.pairingIn_eq_add_of_root_eq_add

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} {N : Type u_5} [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} {S : Type u_6}
  [inst_5 : CommRing S] [inst_6 : Algebra S R] [FaithfulSMul S R] [inst_8 : P.IsValuedIn S] {i j k l : ι},
  P.root k = P.root i + P.root l → P.pairingIn S k j = P.pairingIn S i j + P.pairingIn S l j

Defined in

Mathlib.LinearAlgebra.RootSystem.IsValuedIn

Cited by

2 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCommRingAlgebraFaithfulSMulRootPairing.IsValuedIn