Theorems · Theorem · nonassociative algebras
RootPairing.exists_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) [Nonempty ι]
[NeZero 2], ∃ i, P.root i ≠ 0- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 3 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Function.Embeddingstatement · cited by 988
- RootPairingstatement and proof · cited by 710
- RootPairing.rootstatement · cited by 326
- RootPairing.ne_zeroproof · cited by 32
Cited by3
Results whose statement or proof uses this declaration.
- RootPairing.nontrivialproof · cited by 1
- RootPairing.rootSpan_ne_botproof · cited by 1
- RootPairing.exists_ne_zero'proof · cited by 0