Theorems · Theorem · nonassociative algebras
RootPairing.pairing_same
∀ {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 : ι),
P.pairing i i = 2- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- RootPairingstatement and proof · cited by 710
- RootPairing.pairingstatement · cited by 88
- RootPairing.root_coroot_twoproof · cited by 4
Cited by19
Results whose statement or proof uses this declaration.
- RootPairing.pairingIn_sameproof · cited by 8
- RootPairing.coroot_root_twoproof · cited by 7
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5
- RootPairing.pairing_reflectionPerm_self_rightproof · cited by 4
- RootPairing.pairing_reflectionPerm_self_leftproof · cited by 3
- RootPairing.pairing_smul_root_eq_of_not_linearIndependentproof · cited by 3
- RootPairing.Base.root_sub_root_mem_of_mem_of_memproof · cited by 3
- RootPairing.pairing_one_four_iff'proof · cited by 2
- RootPairing.pairing_two_two_iffproof · cited by 2
- RootPairing.InvariantForm.apply_eq_or_auxproof · cited by 1
- RootPairing.Base.forall_mem_support_invtSubmodule_iffproof · cited by 1