Theorems · Theorem · linear algebra
Module.finrank_pi
∀ (R : Type u) [inst : Semiring R] [StrongRankCondition R] {ι : Type v} [inst_2 : Fintype ι],
Module.finrank R (ι → R) = Fintype.card ιThe finrank of (ι → R) is Fintype.card ι.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- mul_oneproof · cited by 3,885
- Module.finrankstatement · cited by 1,770
- Fintype.cardstatement and proof · cited by 1,386
- Cardinal.liftproof · cited by 583
- StrongRankConditionstatement and proof · cited by 286
- Cardinal.toNatproof · cited by 153
- Cardinal.mk_fintypeproof · cited by 81
- Cardinal.sumproof · cited by 58
- Cardinal.lift_natCastproof · cited by 39
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.finrankproof · cited by 4
- Matrix.rank_le_card_widthproof · cited by 3
- Matrix.rank_le_card_heightproof · cited by 2
- MeasureTheory.volume_sum_rpow_ltproof · cited by 1
- Matrix.rank_oneproof · cited by 1