Theorems · Theorem · linear algebra
Submodule.sup_dualAnnihilator_le_inf
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(U V : Submodule R M), U.dualAnnihilator ⊔ V.dualAnnihilator ≤ (U ⊓ V).dualAnnihilatorSee also Subspace.dualAnnihilator_inf_eq for vector subspaces.
- Defined in
- Mathlib.LinearAlgebra.Dual.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Module.Dualstatement · cited by 583
- Submodule.dualAnnihilatorstatement and proof · cited by 77
- inf_le_infproof · cited by 54
- Submodule.le_dualAnnihilator_dualCoannihilatorproof · cited by 3
- Submodule.le_dualAnnihilator_iff_le_dualCoannihilatorproof · cited by 2
- Submodule.dualCoannihilator_sup_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subspace.dualAnnihilator_inf_eqproof · cited by 2