lean2/tests/lean/run/alias1.lean

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import logic
namespace N1
variable num : Type.{1}
variable foo : num → num → num
end
namespace N2
variable val : Type.{1}
variable foo : val → val → val
end
using N1
using N2
variables a b : num
variables x y : val
check foo a b
check foo x y
variable f : num → val
coercion f
check foo a x
check foo x y
check foo x a
check foo a b
theorem T1 : foo a b = N1.foo a b
:= refl _
definition aux1 := foo a b -- System elaborated it to N2.foo (f a) (f b)
theorem T2 : aux1 = N2.foo (f a) (f b)
:= refl _
using N1
definition aux2 := foo a b -- Now N1 is in the beginning of the queue again, and this is elaborated to N1.foo a b
check aux2
theorem T3 : aux2 = N1.foo a b
:= refl aux2
check foo a b
theorem T4 : foo a b = N1.foo a b
:= refl _