Theorems · Theorem · linear algebra

Module.Basis.range_ofVectorSpace

∀ (K : Type u_3) (V : Type u_4) [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V],
  Set.range ⇑(Module.Basis.ofVectorSpace K V) = Module.Basis.ofVectorSpaceIndex K V

Defined in: Mathlib.LinearAlgebra.Basis.VectorSpace
Cited by: 2 results in Mathlib
Foundations: Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing AddCommGroup Module

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
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
Set.rangestatement · cited by 4,705
Module.Basisstatement · cited by 1,477
DivisionRingstatement and proof · cited by 1,062
Module.Basis.ofVectorSpacestatement · cited by 30
Module.Basis.ofVectorSpaceIndexstatement · cited by 29
Module.Basis.range_extendproof · cited by 1

Cited by2

Results whose statement or proof uses this declaration.

LinearMap.exists_leftInverse_of_injectiveproof · cited by 6
IsNoetherian.range_finsetBasisproof · cited by 0