Theorems · Definition · linear algebra
Subspace.dualAnnihilatorGci
(K : Type u_3) →
(V : Type u_4) →
[inst : Field K] →
[inst_1 : AddCommGroup V] →
[inst_2 : Module K V] →
GaloisCoinsertion (⇑OrderDual.toDual ∘ Submodule.dualAnnihilator)
(Submodule.dualCoannihilator ∘ ⇑OrderDual.ofDual)Submodule.dualAnnihilator and Submodule.dualCoannihilator form a Galois coinsertion.
- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- OrderDualstatement and proof · cited by 927
- Module.Dualstatement and proof · cited by 583
- OrderDual.toDualstatement and proof · cited by 481
- OrderDual.ofDualstatement and proof · cited by 400
- Submodule.dualAnnihilatorstatement and proof · cited by 77
Cited by2
Results whose statement or proof uses this declaration.
- Subspace.dualAnnihilator_injproof · cited by 2
- Subspace.dualAnnihilator_le_dualAnnihilator_iffproof · cited by 0