Theorems · Theorem · nonassociative algebras
RootPairing.Base.linearIndepOn_root
∀ {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} (self : P.Base),
LinearIndepOn R ⇑P.root ↑self.support- Defined in
- Mathlib.LinearAlgebra.RootSystem.Base
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finsetstatement · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement · cited by 8,199
- Function.Embeddingstatement · cited by 988
- RootPairingstatement and proof · cited by 710
- RootPairing.rootstatement · cited by 326
- LinearIndepOnstatement · cited by 211
- RootPairing.Basestatement and proof · cited by 148
- RootPairing.Base.supportstatement · cited by 139
Cited by10
Results whose statement or proof uses this declaration.
- RootPairing.Base.toWeightBasisproof · cited by 8
- RootPairing.Base.flipproof · cited by 8
- RootPairing.Base.height_eq_sumproof · cited by 6
- RootPairing.Base.toWeightBasis_applyproof · cited by 5
- RootPairing.Base.linearIndependent_pair_of_neproof · cited by 2
- RootPairing.Base.pos_or_neg_of_sum_smul_root_memproof · cited by 2
- RootPairing.Base.linearIndependentIntproof · cited by 1
- RootPairing.Base.root_ne_neg_of_neproof · cited by 1
- RootPairing.Base.cartanMatrix_mem_of_neproof · cited by 0
- RootPairing.Base.induction_on_cartanMatrixproof · cited by 0