Theorems · Theorem · linear algebra
rank_fun_infinite
∀ {K : Type u} [inst : DivisionRing K] {ι : Type v} [hι : Infinite ι], Module.rank K (ι → K) = Cardinal.mk (ι → K)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingInfinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- Module.Basisproof · cited by 1,477
- DivisionRingstatement and proof · cited by 1,062
- Function.Embeddingproof · cited by 988
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.aleph0proof · cited by 521
- Module.Basis.reprproof · cited by 498
- Module.rankstatement and proof · cited by 496
- Infinitestatement and proof · cited by 352
Cited by2
Results whose statement or proof uses this declaration.
- rank_dual_eq_card_dual_of_aleph0_le_rank'proof · cited by 2
- rank_dual_eq_card_dual_of_aleph0_le_rankproof · cited by 1