Theorems · Theorem · linear algebra
Subspace.finrank_add_finrank_dualAnnihilator_eq
∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
(W : Subspace K V), Module.finrank K ↥W + Module.finrank K ↥(Submodule.dualAnnihilator W) = Module.finrank K V- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- 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
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- add_commproof · cited by 1,535
- Module.Dualstatement · cited by 583
- Submodule.dualAnnihilatorstatement · cited by 77
- LinearEquiv.finrank_eqproof · cited by 65
Cited by3
Results whose statement or proof uses this declaration.
- RootPairing.isCompl_rootSpan_ker_rootFormproof · cited by 4
- Subspace.finrank_add_finrank_dualCoannihilator_eqproof · cited by 1
- RootPairing.ker_rootForm_eq_dualAnnihilatorproof · cited by 1