Theorems · Theorem · linear algebra
Module.Basis.dual_rank_eq
∀ {R : Type uR} {M : Type uM} {ι : Type uι} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[Finite ι] (b : Module.Basis ι R M), Module.rank R (Module.Dual R M) = Cardinal.lift.{uR, uM} (Module.rank R M)- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finitestatement and proof · cited by 3,029
- Cardinalstatement and proof · cited by 2,598
- Module.Basisstatement and proof · cited by 1,477
- Module.Dualstatement and proof · cited by 583
- Cardinal.liftstatement · cited by 583
- Module.rankstatement and proof · cited by 496
- Cardinal.lift_umaxproof · cited by 56
- Cardinal.lift_id'proof · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- Module.dual_rank_eqproof · cited by 0