English
A weighted sum equals the same when using the indicator function of the subset on the weights.
Русский
Взвешенная сумма равна той же, если веса заменены индикаторной функцией подмножества.
LaTeX
$$$ (s.weightedVSubOfPoint p b w) = ({x \\in s} \\text{ indicador } w).weightedVSubOfPoint p b w $$$
Lean4
/-- A weighted sum of the results of subtracting a default base point
from the given points, as a linear map on the weights. This is
intended to be used when the sum of the weights is 0; that condition
is specified as a hypothesis on those lemmas that require it. -/
def weightedVSub (p : ι → P) : (ι → k) →ₗ[k] V :=
s.weightedVSubOfPoint p (Classical.choice S.nonempty)