Theorems · Theorem · linear algebra
Subspace.dualAnnihilator_dualCoannihilator_eq
∀ {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.dualAnnihilator W).dualCoannihilator = W- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 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.
Cites21
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
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- HasQuotient.Quotientproof · cited by 2,301
- le_antisymmproof · cited by 2,068
- LinearMap.compproof · cited by 1,642
- Module.Dualproof · cited by 583
- Submodule.mkQproof · cited by 232
- Submodule.Quotient.mkproof · cited by 184
- Submodule.dualAnnihilatorstatement · cited by 77
Cited by3
Results whose statement or proof uses this declaration.
- Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iffproof · cited by 2
- Subspace.orderIsoFiniteDimensionalproof · cited by 0
- Subspace.dualAnnihilator_dualAnnihilator_eqproof · cited by 0