Theorems · Theorem · ring theory
Module.natCard_eq_pow_finrank
∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [Module.Finite K V],
Nat.card V = Nat.card K ^ Module.finrank K V- Defined in
- Mathlib.FieldTheory.Finiteness
- Cited by
- 3 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.
Cites14
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
- Module.finrankstatement and proof · cited by 1,770
- Module.Basisproof · cited by 1,477
- DivisionRingstatement and proof · cited by 1,062
- Module.Finitestatement and proof · cited by 1,032
- Nat.cardstatement and proof · cited by 844
- Nat.card_congrproof · cited by 133
- LinearEquiv.toEquivproof · cited by 105
- Module.Basis.equivFunproof · cited by 88
- IsNoetherian.finsetBasisIndexproof · cited by 7
- Module.finrank_eq_nat_card_basisproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.absNorm_eq_pow_inertiaDeg'_of_liesOverproof · cited by 2
- Ideal.cardQuot_pow_inertiaDegproof · cited by 2
- FiniteField.pow_finrank_eq_natCardproof · cited by 2