weightOfEPs — Mathlib

English

If p1.length = p2.length, then p1.comp q1 = p2.comp q2 iff p1 = p2 and q1 = q2.

Русский

Если длины p1 и p2 совпадают, то p1.comp q1 = p2.comp q2 эквивалентно p1 = p2 и q1 = q2.

LaTeX

$$$p_1.length = p_2.length \Rightarrow (p_1.comp\ q_1 = p_2.comp\ q_2) \;\Leftrightarrow\; (p_1 = p_2) \land (q_1 = q_2)$$$

Lean4

/-- The weight of a path, where the weight of an edge is defined by a function on its endpoints. -/
@[to_additive addWeightOfEPs /-- The additive weight of a path, where the weight of an edge is
    defined by a function on its endpoints. -/
    ]
def weightOfEPs (w : V → V → R) : ∀ {i j : V}, Path i j → R :=
  weight (fun {i j} (_ : i ⟶ j) => w i j)

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