rw [w_cast, TotalDFA.in_language_iff_del_star_final]
case h
α qs : Type
M : DFA α qs
w : Word { x // x ∈ M.Z }
w' : Word { x // x ∈ (DFA.toTotalDFA M).Z } := w
w_cast : w = w'
⊢ (∃ qf ∈ DFA.del_star M (M.q₀, w), qf ∈ M.F) ↔ w ∈ DFA.AcceptedLanguage (DFA.toTotalDFA M).toDFA
case h
α qs : Type
M : DFA α qs
w : Word { x // x ∈ M.Z }
w' : Word { x // x ∈ (DFA.toTotalDFA M).Z } := w
w_cast : w = w'
⊢ (∃ qf ∈ DFA.del_star M (M.q₀, w'), qf ∈ M.F) ↔
    TotalDFA.del_star' (DFA.toTotalDFA M) ((DFA.toTotalDFA M).q₀, w') ∈ (DFA.toTotalDFA M).F