English
Equality on all uniformly bounded paths is decidable given decidable equality on vertices and arrows.
Русский
Равенство на всех ограниченно ограниченных путях разрешимо при условии разбора равенства вершин и стрел.
LaTeX
$$$\\mathrm{DecidableEqBoundedPaths}[\\text{DecidableEq } V][\\forall a,b,\\ DecidableEq (a\\to b)](n) : (v,w:V)\\to\\mathrm{DecidableEq}(\\mathrm{BoundedPaths}(v,w,n)).$$$
Lean4
/-- Equality is decidable on all uniformly bounded paths given decidable
equality on the vertices and the arrows. -/
instance decidableEqBoundedPaths [DecidableEq V] [∀ (v w : V), DecidableEq (v ⟶ w)] (n : ℕ) :
(v w : V) → DecidableEq (BoundedPaths v w n) :=
n.rec decidableEqBddPathsZero fun n decEq => decidableEqBddPathsOfDecidableEq n inferInstance inferInstance decEq
