Theorems · Definition · linear algebra
Module.Basis.ofVectorSpaceIndex
(K : Type u_3) → (V : Type u_4) → [inst : DivisionRing K] → [inst_1 : AddCommGroup V] → [Module K V] → Set V
A set used to index Basis.ofVectorSpace.
- Defined in
- Mathlib.LinearAlgebra.Basis.VectorSpace
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- DivisionRingstatement and proof · cited by 1,062
- LinearIndepOn.extendproof · cited by 28
Cited by32
Results whose statement or proof uses this declaration.
- Module.Basis.ofVectorSpacestatement · cited by 30
- Submodule.eq_top_of_finrank_eqproof · cited by 15
- LinearMap.exists_leftInverse_of_injectiveproof · cited by 6
- IsNoetherian.finsetBasisproof · cited by 5
- Module.Basis.coe_ofVectorSpacestatement and proof · cited by 4
- LocallyBoundedVariationOn.ae_differentiableWithinAt_of_memproof · cited by 4
- coevaluationproof · cited by 4
- Module.Basis.ofVectorSpace_apply_selfstatement and proof · cited by 3
- coevaluation_apply_onestatement and proof · cited by 3
- Module.Basis.exists_basisproof · cited by 2
- lipschitzExtensionConstant_defstatement and proof · cited by 2
- Module.Basis.range_ofVectorSpacestatement · cited by 2