sum_affineCombinationSingleWeights

English

For any index i, the weight function with i on both sides is zero.

Русский

Для любого i веса с одинаковыми индексами даёт ноль.

LaTeX

$$$ weightedVSubVSubWeights\ k\ i\ i = 0 $$$

Lean4

@[simp]
theorem sum_affineCombinationSingleWeights [DecidableEq ι] {i : ι} (h : i ∈ s) :
    ∑ j ∈ s, affineCombinationSingleWeights k i j = 1 :=
  by
  rw [← affineCombinationSingleWeights_apply_self k i]
  exact sum_eq_single_of_mem i h fun j _ hj => affineCombinationSingleWeights_apply_of_ne k hj

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