Theorems · Theorem · linear algebra
Subspace.dual_finrank_eq
∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V],
Module.finrank K (Module.Dual K V) = Module.finrank K V- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 100 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.
Cites18
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
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- FiniteDimensionalproof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- Module.Basisproof · cited by 1,477
- LinearEquiv.symmproof · cited by 1,461
- Module.Dualstatement and proof · cited by 583
Cited by5
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
- RootPairing.rootSpan_eq_top_iffproof · cited by 1
- LinearMap.finrank_range_dualMap_eq_finrank_rangeproof · cited by 1