definition foo [forward] : ∀ (m n k : ℕ), P (f m) → P (g n) → P (f k) → P k ∧ R (g m) (f n) ∧ P (g m) ∧ P (f n) :=
λ (m n k : ℕ), sorry
(multi-)patterns:
?M_1 : ℕ, ?M_2 : ℕ, ?M_3 : ℕ
{P ?M_3, R (g ?M_1) (f ?M_2)}