clear a2_right
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
xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a r)
a2_right : ∃ s_1 ∈ RegExp.languageOf α s, xs ++ s_1 = w
ys : List α
a3 : ys ∈ RegExp.languageOf α s ∧ xs ++ ys = w
⊢ ∃ r_1 ∈ RegExp.languageOf α r, ∃ s_1 ∈ RegExp.languageOf α s, r_1 ++ s_1 = a :: w
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
xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a r)
ys : List α
a3 : ys ∈ RegExp.languageOf α s ∧ xs ++ ys = w
⊢ ∃ r_1 ∈ RegExp.languageOf α r, ∃ s_1 ∈ RegExp.languageOf α s, r_1 ++ s_1 = a :: w