Theorems · Theorem · ring theory
Module.card_eq_pow_finrank
∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [inst_3 : Fintype K]
[inst_4 : Fintype V], Fintype.card V = Fintype.card K ^ Module.finrank K V- Defined in
- Mathlib.FieldTheory.Finiteness
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fintypestatement and proof · cited by 7,736
- Module.finrankstatement and proof · cited by 1,770
- Module.Basisproof · cited by 1,477
- Fintype.cardstatement and proof · cited by 1,386
- DivisionRingstatement and proof · cited by 1,062
- Module.finrank_eq_card_basisproof · cited by 40
- IsNoetherian.finsetBasisIndexproof · cited by 7
- IsNoetherian.finsetBasisproof · cited by 5
- Module.card_fintypeproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- FiniteField.orderOf_frobeniusAlgHomproof · cited by 3
- FiniteField.nonempty_algHom_of_finrank_dvdproof · cited by 3
- GaloisField.finrankproof · cited by 2
- card_linearIndependentproof · cited by 1