constructor
graph✝ : Graph
a✝ : Class graph✝
path₁ path₂ : Path graph✝ a✝
⊢ path₁ ≂ path₂ ↔ prefix? path₁ = prefix? path₂
case mp
graph✝ : Graph
a✝ : Class graph✝
path₁ path₂ : Path graph✝ a✝
⊢ path₁ ≂ path₂ → prefix? path₁ = prefix? path₂

case mpr
graph✝ : Graph
a✝ : Class graph✝
path₁ path₂ : Path graph✝ a✝
⊢ prefix? path₁ = prefix? path₂ → path₁ ≂ path₂