obtain ⟨i', pcs, scs, eqs, path, step⟩ := path
next i : ℕ
cs : List Char
nfa : NFA
start : ℕ
path : nfa.pathToNext next start i cs
⊢ nfa.pathIn (min start next) i next cs
case intro.intro.intro.intro.intro
next i : ℕ
cs : List Char
nfa : NFA
start i' : ℕ
pcs scs : List Char
eqs : cs = pcs ++ scs
path : nfa.pathIn start i i' pcs
step : nfa.stepIn start i' next scs
⊢ nfa.pathIn (min start next) i next cs