Theorems · Theorem · linear algebra
Submodule.dualCoannihilator_iSup_eq
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Sort u_3}
(U : ι → Submodule R (Module.Dual R M)), (⨆ i, U i).dualCoannihilator = ⨅ i, (U i).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.
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
- iSupstatement · cited by 2,415
- iInfstatement · cited by 1,690
- Module.Dualstatement and proof · cited by 583
- Submodule.dualCoannihilatorstatement · cited by 41
- GaloisConnection.u_iInfproof · cited by 40
- Submodule.dualAnnihilator_gcproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.iSup_dualAnnihilator_le_iInfproof · cited by 0