Theorems · Theorem · nonassociative algebras

RootPairing.coxeterWeightIn_ne_four

∀ {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) (S : Type u_5)
  {i j : ι} [Finite ι] [CharZero R] [IsDomain R] [Module.IsTorsionFree R M] [inst_9 : CommRing S]
  [inst_10 : Algebra S R] [FaithfulSMul S R] [inst_12 : P.IsValuedIn S] [P.IsReduced],
  i ≠ j → P.root i ≠ -P.root j → P.coxeterWeightIn S i j ≠ 4

Defined in: Mathlib.LinearAlgebra.RootSystem.Reduced
Cited by: 1 results in Mathlib
Foundations: Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module Finite CharZero IsDomain Module.IsTorsionFree CommRing Algebra FaithfulSMul RootPairing.IsValuedIn RootPairing.IsReduced

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

DFunLike.coestatement and proof · 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
Algebrastatement and proof · cited by 11,388
Finitestatement and proof · cited by 3,029
IsDomainstatement and proof · cited by 2,196
Function.Embeddingstatement · cited by 988
CharZerostatement and proof · cited by 932
RootPairingstatement and proof · cited by 710
Module.IsTorsionFreestatement and proof · cited by 600
FaithfulSMulstatement and proof · cited by 340

Cited by1

Results whose statement or proof uses this declaration.

RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRedproof · cited by 6