Theorems · Theorem · linear algebra
Module.finrank_finsupp_self
∀ (R : Type u) [inst : Semiring R] [StrongRankCondition R] {ι : Type v} [inst_2 : Fintype ι],
Module.finrank R (ι →₀ R) = Fintype.card ιThe finrank of (ι →₀ R) is Fintype.card ι.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 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.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- Finsuppstatement and proof · cited by 5,255
- Cardinalproof · cited by 2,598
- Module.finrankstatement · cited by 1,770
- Fintype.cardstatement and proof · cited by 1,386
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
- StrongRankConditionstatement and proof · cited by 286
- Cardinal.toNatproof · cited by 153
- Cardinal.toNat_liftproof · cited by 41
Cited by3
Results whose statement or proof uses this declaration.
- Subalgebra.LinearDisjoint.of_finrank_sup_of_freeproof · cited by 2
- Module.exists_basis_of_basis_baseChangeproof · cited by 1
- Module.Free.away_of_finite_of_flat_of_rankAtStalk_constantproof · cited by 0