sum_touchpointWeights — Mathlib

English

The self-weight in the touchpoint weights is zero.

Русский

Вес касательных точек на диагонали i = j равно нулю.

LaTeX

$$$ s.touchpointWeights(\text{signs}, i, i) = 0 $$$

Lean4

@[simp]
theorem sum_touchpointWeights (signs : Finset (Fin (n + 1))) (i : Fin (n + 1)) :
    ∑ j, s.touchpointWeights signs i j = 1 :=
  (eq_affineCombination_of_mem_affineSpan_of_fintype (s.touchpoint_mem_affineSpan_simplex signs i)).choose_spec.1

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