touchpointWeights_singleton_neg — Mathlib

English

For i ≠ j, the sign of s.touchpointWeights { i } j i equals -1 (consistent sign):

Русский

Для i ≠ j знак s.touchpointWeights { i } j i равен -1.

LaTeX

$$$\operatorname{sign}\bigl(s.touchpointWeights\{i\} j i\bigr) = -1\quad (i \neq j)$$$

Lean4

theorem touchpointWeights_singleton_neg [Nat.AtLeastTwo n] {i j : Fin (n + 1)} (hne : i ≠ j) :
    s.touchpointWeights { i } j i < 0 := by simpa [sign_eq_neg_one_iff] using s.sign_touchpointWeights_singleton_neg hne

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