Theorems · Theorem · nonassociative algebras
RootPairing.isCompl_rootSpan_ker_rootForm
∀ {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], IsCompl (P.rootSpan R) (LinearMap.ker P.RootForm)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- Module.finrankproof · cited by 1,770
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- LinearMap.kerstatement and proof · cited by 848
- RootPairingstatement and proof · cited by 710
Cited by4
Results whose statement or proof uses this declaration.
- RootPairing.orthogonal_rootSpan_eqproof · cited by 1
- RootPairing.ker_rootForm_eq_dualAnnihilatorproof · cited by 1
- RootPairing.isCompl_corootSpan_ker_corootFormproof · cited by 0
- RootPairing.rootForm_restrict_nondegenerate_of_isAnisotropicproof · cited by 0