intro xs x a1
case mpr
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p_0 q_0 : σ_0
⊢ ∀ (x : List σ_0),
    { start_state := p_0, symbol := c, stop_state_list := x } ∈ M_0.symbol_arrow_list →
      q_0 ∈ x →
        ∃ stop_state_list,
          (∃ a ∈ M_0.symbol_arrow_list,
              a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
            Sum.inl q_0 ∈ stop_state_list
case mpr
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p_0 q_0 : σ_0
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ ∃ stop_state_list,
    (∃ a ∈ M_0.symbol_arrow_list,
        a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
      Sum.inl q_0 ∈ stop_state_list