lean2/tests/lean/run/e12.lean

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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
constants n m : nat.nat
constants i j : int.int
section
open [notations] nat
open [notations] int
open [decls] nat
open [decls] int
check n+m
check i+j
-- check i+n -- Error
end
namespace int
open [decls] nat (nat)
-- 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
end int
section
open [notations] nat
open [notations] int
open [declarations] nat
open [declarations] int
check n+m
check i+n
check n+i
end
section
open nat
open int
check n+m
check i+n
end