What is atticus tryng to prove in the court proceedings when he has the sheriff testify about which side of the face Mayella was injured on?

When Atticus called the sheriff, Heck Tate, he establishes
for the jury the injuries that Mayella suffered in the attack.  She has bruises all
around her neck and on the right side of her face.  These injuries show that she was
strangled by two hands and beaten on the right side of her face by a person who leads
with his left.

Atticus gets Bob Ewell to confirm the
testimony of Heck Tate.  He doesn't dispute anything the sheriff says.  Then Atticus
gets Heck Tate to sign his name.  Although Bob thinks Atticus is doing this to prove he
can't write, he's really doing it to show that Bob is
left-handed.

When Tom Robinson testifies later in the trial
(the same night), it is apparent to everyone, including the jury, that Tom could not be
guilty of attacking Mayella in this way.  His left arm is completely useless.  It hangs
weakly by his side because all the muscles were torn from the bone in a cotton gin
accident years ago.

Atticus has successfully proven in the
minds of the jury and spectators that Tom is not guilty.  Although he doesn't win the
case, Atticus has revealed the truth.