Theorems · Theorem · nonassociative algebras

RootPairing.coxeterWeightIn_mem_set_of_isCrystallographic

∀ {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) [Finite ι]
  [CharZero R] [inst_7 : P.IsCrystallographic] (i j : ι), P.coxeterWeightIn ℤ i j ∈ {0, 1, 2, 3, 4}

Defined in: Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas
Cited by: 2 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module Finite CharZero RootPairing.IsCrystallographic

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Cites16

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

Setstatement · cited by 53,352
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
Finitestatement and proof · cited by 3,029
Nat.cast_oneproof · cited by 2,501
Nat.cast_zeroproof · cited by 1,870
CharZerostatement and proof · cited by 932
RootPairingstatement and proof · cited by 710
Fintype.ofFiniteproof · cited by 255
RootPairing.IsCrystallographicstatement and proof · cited by 160

Cited by2

Results whose statement or proof uses this declaration.

RootPairing.pairingIn_pairingIn_mem_set_of_isCrystallographicproof · cited by 7
RootPairing.root_sub_root_mem_of_pairingIn_posproof · cited by 7