intro s a1 a2
case h.a.mpr
α σ : Type
N : NA α σ
cs : List α
⊢ ∀ x ∈ N.evalFrom N.startingStates cs,
    x ∈ N.acceptingStates →
      ∃
        s ∈
          { step := N.stepSet, startingState := N.startingStates,
                acceptingStates := {S | ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom
            N.startingStates cs,
        s ∈ N.acceptingStates
case h.a.mpr
α σ : Type
N : NA α σ
cs : List α
s : σ
a1 : s ∈ N.evalFrom N.startingStates cs
a2 : s ∈ N.acceptingStates
⊢ ∃
    s ∈
      { step := N.stepSet, startingState := N.startingStates,
            acceptingStates := {S | ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom
        N.startingStates cs,
    s ∈ N.acceptingStates