Theorems · Theorem · nonassociative algebras

RootPairing.EmbeddedG2.pairingIn_twoShortAddLong_right

∀ {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)
  [inst_5 : P.EmbeddedG2] [Finite ι] [CharZero R] [IsDomain R] (i : ι),
  P.pairingIn ℤ i (RootPairing.EmbeddedG2.twoShortAddLong P) =
    2 * P.pairingIn ℤ i (RootPairing.EmbeddedG2.short P) + 3 * P.pairingIn ℤ i (RootPairing.EmbeddedG2.long P)

Defined in: Mathlib.LinearAlgebra.RootSystem.Finite.G2
Cited by: 1 results in Mathlib
Foundations: Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module RootPairing.EmbeddedG2 Finite CharZero IsDomain

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DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Fintypeproof · cited by 7,736
Algebra.algebraMapproof · cited by 4,706
Finitestatement and proof · cited by 3,029
IsDomainstatement and proof · cited by 2,196
mul_assocproof · cited by 1,667
map_mulproof · cited by 1,137
map_addproof · cited by 964
CharZerostatement and proof · cited by 932

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RootPairing.EmbeddedG2.isOrthogonal_short_and_longproof · cited by 2