Theorems · Theorem · geometry

AffineBasis.exists_affineBasis_of_finiteDimensional

∀ {ι : Type u₁} {k : Type u₂} {V : Type u₃} {P : Type u₄} [inst : AddCommGroup V] [inst_1 : AddTorsor V P]
  [inst_2 : DivisionRing k] [inst_3 : Module k V] [inst_4 : Fintype ι] [FiniteDimensional k V],
  Fintype.card ι = Module.finrank k V + 1 → Nonempty (AffineBasis ι k P)

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

1 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddTorsorDivisionRingModuleFintypeFiniteDimensional