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[Keiko Nakata <keiko AT kurims.kyoto-u.ac.jp>]

Hello,

How can I prove the following goal? 
It looked so obvious that I thought auto would handle.

Goal forall (f: nat -> nat) (n: nat * nat),
let (n1, _) := n in f n1 = f (let (n1, _) := n in n1).

I was blocked when trying to prove the following a little bit more 
complicated goal with apply "hypothesis", assuming seemingly obvious
conversions. 

Goal forall (p : nat -> Prop) (f : nat -> nat) (n : nat * nat),
(let (n1, _) := n in p (f n1)) -> p (f (let (n1, _) := n in n1)).
intros p f n h. apply h.

With best regards,
Keiko