Theorems · Theorem · nonassociative algebras
RootPairing.ne_zero
∀ {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) [NeZero 2],
P.root i ≠ 0- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- map_zeroproof · cited by 1,614
- Function.Embeddingstatement · cited by 988
- RootPairingstatement and proof · cited by 710
- RootPairing.rootstatement and proof · cited by 326
- RootPairing.corootproof · cited by 123
- RootPairing.toLinearMapproof · cited by 108
- RootPairing.root_coroot_twoproof · cited by 4
Cited by32
Results whose statement or proof uses this declaration.
- RootPairing.pairing_eq_zero_iffproof · cited by 7
- RootPairing.Base.exists_root_eq_sum_intproof · cited by 7
- RootPairing.Base.sub_notMem_range_rootproof · cited by 5
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5
- RootPairing.nsmul_notMem_range_rootproof · cited by 4
- RootPairing.Base.height_ne_zeroproof · cited by 4
- RootPairing.exists_ne_zeroproof · 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.eq_baseOf_of_linearIndepOn_of_mem_or_neg_mem_closureproof · cited by 2
- RootPairing.GeckConstruction.isNilpotent_eproof · cited by 2
- RootPairing.zero_notMem_range_rootproof · cited by 2