Theorems · Theorem · linear algebra
Subspace.dualAnnihilator_iInf_eq
∀ {K : Type u_1} {V₁ : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V₁] [inst_2 : Module K V₁] {ι : Type u_4}
[Finite ι] (W : ι → Subspace K V₁), Submodule.dualAnnihilator (⨅ i, W i) = ⨆ i, Submodule.dualAnnihilator (W i)- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Equivproof · cited by 8,337
- Fintypeproof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Bot.botproof · cited by 4,720
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.iInf_ker_weight_eq_botproof · cited by 2