Theorems · Theorem · geometry

AffineBasis.affineCombination_coord_eq_self

∀ {ι : Type u_1} {k : Type u_5} {V : Type u_6} {P : Type u_7} [inst : AddCommGroup V] [inst_1 : AddTorsor V P]
  [inst_2 : Ring k] [inst_3 : Module k V] (b : AffineBasis ι k P) [inst_4 : Fintype ι] (q : P),
  ((Finset.affineCombination k Finset.univ ⇑b) fun i => (b.coord i) q) = q

Defined in

Mathlib.LinearAlgebra.AffineSpace.Basis

Cited by

3 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddTorsorRingModuleFintype