Theorems · Theorem · linear algebra
Module.finite_of_finrank_pos
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M]
[StrongRankCondition R], 0 < Module.finrank R M → Module.Finite R M- Defined in
- Mathlib.LinearAlgebra.Dimension.Free
- Cited by
- 8 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.
Cites8
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
- Module.finrankstatement and proof · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- Module.Freestatement and proof · cited by 597
- StrongRankConditionstatement and proof · cited by 286
- Module.finrank_of_not_finiteproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- FiniteDimensional.of_finrank_posproof · cited by 8
- Module.finite_of_finrank_eq_succproof · cited by 4
- FiniteField.nonempty_algHom_of_finrank_dvdproof · cited by 3
- Module.Free.bijective_algebraMap_of_finrank_eq_oneproof · cited by 1
- eq_span_singleton_of_mem_of_finrank_eq_oneproof · cited by 1
- Subalgebra.LinearDisjoint.of_finrank_coprime_of_freeproof · cited by 1
- FunctionField.finiteDimensional_of_constantExtensionproof · cited by 0
- Module.Basis.nonempty_unique_index_of_finrank_eq_oneproof · cited by 0