Now we use process of elimination.
If b-a = 0 then this implies that b = a and then b2.=.a2
which contradicts the given statement
If -(b-a) > 0 then a-b > 0 which implies that b.<.a. Therefore b2.<.a2 .(from 8) which also contradict the statement that a2.<.b2.
Hence b-a > 0 which implies that a.<.b.
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