42 lines
704 B
Text
42 lines
704 B
Text
import data.nat
|
|
open nat
|
|
|
|
definition f (a b : nat) := a + b
|
|
|
|
example (a b : nat) : f a b = 0 → f b a = 0 :=
|
|
begin
|
|
intro h,
|
|
unfold f at h,
|
|
state,
|
|
unfold f,
|
|
state,
|
|
rewrite [add.comm],
|
|
exact h
|
|
end
|
|
|
|
example (a b : nat) : f a b = 0 → f b a = 0 :=
|
|
begin
|
|
intro h,
|
|
unfold f at *,
|
|
state,
|
|
rewrite [add.comm],
|
|
exact h
|
|
end
|
|
|
|
example (a b c : nat) : f c c = 0 → f a b = 0 → f b a = f c c :=
|
|
begin
|
|
intros [h₁, h₂],
|
|
unfold f at (h₁, h₂),
|
|
state,
|
|
unfold f,
|
|
rewrite [add.comm, h₁, h₂],
|
|
end
|
|
|
|
example (a b c : nat) : f c c = 0 → f a b = 0 → f b a = f c c :=
|
|
begin
|
|
intros [h₁, h₂],
|
|
unfold f at * ⊢,
|
|
state,
|
|
unfold f,
|
|
rewrite [add.comm, h₁, h₂],
|
|
end
|