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3.9, No 4.
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The formula has the form of:

   some A ==> (forall i: 0<=i : a[i]=a[0])
   
You can prove this by assuming A, and then proving the RHS
of the implication above.  As hinted, you can prove the latter
using induction. Now, the Induction rule for natural numbers 
look like this:

    (1)    P 0
    (2)   (forall n : n>=0 : P n ==> P (n + 1))
          --------------------------------------
          (forall n : n>=0 : P n)
          
And what is "P" in this case?

Spoiler: define P i to represent (a[i]=a[0]).