Theorems · Theorem · linear algebra
Module.finite_of_rank_eq_nat
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M]
{n : ℕ}, Module.rank R M = ↑n → Module.Finite R M- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Finiteproof · cited by 3,029
- Cardinalstatement · cited by 2,598
- Nontrivialproof · cited by 2,416
- Module.Basisproof · cited by 1,477
- Module.Finitestatement · cited by 1,032
- LE.le.trans_ltproof · cited by 795
- Module.Freestatement and proof · cited by 597
- Module.rankstatement and proof · cited by 496
- LE.le.trans_eqproof · cited by 328
Cited by2
Results whose statement or proof uses this declaration.
- Module.finite_of_rank_eq_oneproof · cited by 1
- FiniteDimensional.of_rank_eq_natproof · cited by 0