lean2/tests/lean/run/class5.lean

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import logic
namespace algebra
inductive mul_struct [class] (A : Type) : Type :=
mk : (A → A → A) → mul_struct A
definition mul {A : Type} [s : mul_struct A] (a b : A)
:= mul_struct.rec (λ f, f) s a b
infixl `*` := mul
end algebra
open algebra
namespace nat
inductive nat : Type :=
zero : nat,
succ : nat → nat
constant mul : nat → nat → nat
constant add : nat → nat → nat
definition mul_struct [instance] : algebra.mul_struct nat
:= algebra.mul_struct.mk mul
end nat
section
open algebra nat
variables a b c : nat
check a * b * c
definition tst1 : nat := a * b * c
end
section
open [notation] algebra
open nat
-- check mul_struct nat << This is an error, we are open only the notation from algebra
variables a b c : nat
check a * b * c
definition tst2 : nat := a * b * c
end
section
open nat
-- check mul_struct nat << This is an error, we are open only the notation from algebra
variables a b c : nat
check #algebra a*b*c
definition tst3 : nat := #algebra a*b*c
end
section
open nat
set_option pp.implicit true
definition add_struct [instance] : algebra.mul_struct nat
:= algebra.mul_struct.mk add
variables a b c : nat
check #algebra a*b*c -- << is open add instead of mul
definition tst4 : nat := #algebra a*b*c
end