definition lemma1 : ∀ (a : ℕ), r a → s a → p a :=
λ (a : ℕ) (H.1 : r a) (H.2 : s a), rq₁ a H.1
definition lemma2 : ∀ (a : ℕ), r a → s a → p a :=
λ (a : ℕ) (H.1 : r a), rq₂ a