Theorems · Theorem · nonassociative algebras
RootPairing.linearIndepOn_coroot_iff
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Fintype ι] [inst_1 : AddCommGroup M]
[inst_2 : AddCommGroup N] [inst_3 : Field R] [inst_4 : Module R M] [inst_5 : Module R N] (P : RootPairing ι R M N)
[P.IsAnisotropic] [P.IsRootSystem] [NeZero 2] {s : Set ι}, LinearIndepOn R (⇑P.coroot) s ↔ LinearIndepOn R (⇑P.root) s- Cited by
- 0 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Function.Embeddingstatement · cited by 988
- RootPairingstatement and proof · cited by 710
- RootPairing.rootstatement · cited by 326
- LinearIndepOnstatement · cited by 211
- RootPairing.corootstatement · cited by 123
- RootPairing.flipproof · cited by 79
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.