Theorems · Theorem · linear algebra
Module.Basis.exists_basis
∀ (K : Type u_3) (V : Type u_4) [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V], ∃ s, Nonempty (Module.Basis (↑s) K V)
- Defined in
- Mathlib.LinearAlgebra.Basis.VectorSpace
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 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.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.Elemstatement · cited by 7,166
- Module.Basisstatement · cited by 1,477
- DivisionRingstatement and proof · cited by 1,062
- Module.Basis.ofVectorSpaceproof · cited by 30
- Module.Basis.ofVectorSpaceIndexproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.linearDisjoint_of_isPurelyInseparable_of_isSeparableproof · cited by 2
- LocallyCompactSpace.of_finiteDimensional_of_completeproof · cited by 1