weightOfEPs_cons — Mathlib

English

WeightOfEPs is multiplicative along path extension: weightOfEPs w (p.cons e) = weightOfEPs w p · w(b,c).

Русский

Вес концовPath-расширения умножается на вес добавляемого ребра: weightOfEPs w (p.cons e) = weightOfEPs w p · w(b,c).

LaTeX

$$$\mathrm{weightOfEPs}\ w\ (p.\mathrm{cons}\ e) = \mathrm{weightOfEPs}\ w\ p \cdot w\; b\; c$$$

Lean4

@[to_additive addWeightOfEPs_cons]
theorem weightOfEPs_cons (w : V → V → R) {a b c : V} (p : Path a b) (e : b ⟶ c) :
    weightOfEPs w (p.cons e) = weightOfEPs w p * w b c := by unfold weightOfEPs; simp

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