import data.nat open algebra example (a b : Prop) : a → b → a ∧ b := begin intro Ha, intro Hb, let aux := and.intro Ha Hb, exact aux end open nat example (a b : nat) : a > 0 → b > 0 → a + b + 0 > 0 := begin intro agt0, intro bgt0, let H := add_pos agt0 bgt0, change a + b > 0, exact H end