simp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ w ∈ {x | ∃ r_1 ∈ RegExp.languageOf α r.delta, ∃ s_1 ∈ RegExp.languageOf α (RegExp.derivative a s), r_1 ++ s_1 = x} ↔
    a :: w ∈ {x | ∃ r_1 ∈ RegExp.languageOf α r, ∃ s_1 ∈ RegExp.languageOf α s, r_1 ++ s_1 = x}
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.languageOf α r.delta, ∃ s_1 ∈ RegExp.languageOf α (RegExp.derivative a s), r_1 ++ s_1 = w) ↔
    ∃ r_1 ∈ RegExp.languageOf α r, ∃ s_1 ∈ RegExp.languageOf α s, r_1 ++ s_1 = a :: w