lean2/tests/lean/run/e11.lean

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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
section
-- Open "only" the notation and declarations from the namespaces nat and int
open [notation] nat
open [notation] int
open [decls] nat
open [decls] int
variables n m : nat
variables 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 add_ni
check i + n
check n + i
end