Theorems · Theorem · linear algebra
Subspace.comap_dualAnnihilator_dualAnnihilator
∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] (W : Subspace K V),
Submodule.comap (Module.Dual.eval K V) (Submodule.dualAnnihilator W).dualAnnihilator = W- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 1 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.
Cites13
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
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- Module.Dualstatement and proof · cited by 583
- Submodule.comapstatement and proof · cited by 347
- Submodule.extproof · cited by 204
- Submodule.dualAnnihilatorstatement and proof · cited by 77
- Subspacestatement and proof · cited by 56
- Module.Dual.evalstatement and proof · cited by 52
Cited by1
Results whose statement or proof uses this declaration.
- Subspace.map_le_dualAnnihilator_dualAnnihilatorproof · cited by 1