prelude
precedence `+`:65

namespace nat
  constant nat : Type.{1}
  constant add : nat → nat → nat
  infixl + := add
end nat

namespace int
  open nat (nat)
  constant int : Type.{1}
  constant add : int → int → int
  infixl + := add
  constant of_nat : nat → int
  coercion of_nat
end int

-- Open "only" the notation and declarations from the namespaces nat and int
open [notation] nat
open [notation] int
open [decls] nat
open [decls] int

constants n m : nat
constants i j : int
check n + m
check i + j

-- The following check does not work, since we are not open the coercions
-- check n + i

-- Here is a possible trick for this kind of configuration
definition add_ni (a : nat) (b : int) := (of_nat a) + b
definition add_in (a : int) (b : nat) := a + (of_nat b)
infixl + := add_ni
infixl + := add_in

check i + n
check n + i