Theorems · Theorem · linear algebra
finrank_eq_zero_of_basis_imp_not_finite
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M],
(∀ (s : Set M) (a : Module.Basis (↑s) R M), ¬s.Finite) → Module.finrank R M = 0- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemstatement and proof · cited by 7,166
- Finsuppproof · cited by 5,255
- Nontrivialproof · cited by 2,416
- Set.Finitestatement and proof · cited by 1,814
- Module.finrankstatement · cited by 1,770
- Module.Basisstatement and proof · cited by 1,477
- Module.Freestatement and proof · cited by 597
- Infiniteproof · cited by 352
Cited by2
Results whose statement or proof uses this declaration.
- finrank_eq_zero_of_basis_imp_falseproof · cited by 3
- finrank_eq_zero_of_not_exists_basis_finiteproof · cited by 0