Theorems · Theorem · linear algebra
Module.dual_rank_eq
∀ {K : Type uK} {V : Type uV} [inst : CommSemiring K] [inst_1 : AddCommMonoid V] [inst_2 : Module K V] [Module.Free K V]
[Module.Finite K V], Module.rank K (Module.Dual K V) = Cardinal.lift.{uK, uV} (Module.rank K V)- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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
- Cardinalstatement · cited by 2,598
- Module.Finitestatement and proof · cited by 1,032
- Module.Freestatement and proof · cited by 597
- Module.Dualstatement · cited by 583
- Cardinal.liftstatement · cited by 583
- Module.rankstatement · cited by 496
- Module.Free.chooseBasisproof · cited by 121
- Module.Basis.dual_rank_eqproof · cited by 1
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