import data.nat logic.inhabited open nat inhabited constant N : Type.{1} constant a : N section s1 set_option pp.implicit true definition f (a b : nat) := a theorem nat_inhabited [instance] : inhabited nat := inhabited.mk zero definition to_N [coercion] (n : nat) : N := a infixl `$$`:65 := f end s1 theorem tst : inhabited nat constants n m : nat check n = a