Theorems · Theorem · linear algebra
Module.finrank_fin_fun
∀ (R : Type u) [inst : Semiring R] [StrongRankCondition R] {n : ℕ}, Module.finrank R (Fin n → R) = nThe vector space of functions on Fin n has finrank equal to n.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringStrongRankCondition
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Module.finrankstatement · cited by 1,770
- StrongRankConditionstatement and proof · cited by 286
- Fintype.card_finproof · cited by 270
- Module.finrank_fintype_fun_eq_cardproof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- FiniteDimensional.completeproof · cited by 29
- FiniteDimensional.properproof · cited by 4
- Real.dimH_of_mem_nhdsproof · cited by 3
- contDiffOn_clm_applyproof · cited by 2
- continuousWithinAt_clm_applyproof · cited by 0