Theorems · Theorem · nonassociative algebras
RootPairing.isOrthogonal_comm
∀ {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) (i j : ι),
P.IsOrthogonal i j → Commute (P.reflection i) (P.reflection j)- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
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- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearEquivstatement · cited by 3,317
- sub_zeroproof · cited by 938
- zero_smulproof · cited by 716
- RootPairingstatement and proof · cited by 710
- Commutestatement · cited by 639
- map_smulproof · cited by 566
- map_subproof · cited by 565
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