Theorems · Theorem · convex and discrete geometry

Finset.centerMass_congr

∀ {R : Type u_1} {E : Type u_3} {ι : Type u_5} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
  {t : Finset ι} {w : ι → R} {z : ι → E} [inst_3 : DecidableEq ι] {t' : Finset ι} {w' : ι → R} {z' : ι → E},
  (∀ (i : ι), i ∈ t ∧ w i ≠ 0 ∨ i ∈ t' ∧ w' i ≠ 0 → i ∈ t ∩ t' ∧ w i = w' i ∧ z i = z' i) →
    t.centerMass w z = t'.centerMass w' z'

Defined in

Mathlib.Analysis.Convex.Combination

Cited by

3 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleDecidableEq