Theorems · Theorem · linear algebra
Submodule.dualCoannihilator_sup_eq
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(U V : Submodule R (Module.Dual R M)), (U ⊔ V).dualCoannihilator = U.dualCoannihilator ⊓ V.dualCoannihilator- Defined in
- Mathlib.LinearAlgebra.Dual.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 583
- Submodule.dualCoannihilatorstatement · cited by 41
- GaloisConnection.u_infproof · cited by 37
- Submodule.dualAnnihilator_gcproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.sup_dualAnnihilator_le_infproof · cited by 1