To obtain a contradiction, we suppose that ......

Suppose, to derive a contradiction, that ......

Striving for a contradiction, suppose that ......

Aiming for a contradiction, suppose that ......

Suppose, towards a contradiction $\langle$for contradiction$\rangle$, that ......

......, which is a contradiction.

Now we have the required contradiction since ......

This leads to the contradiction that $0<a<b=0$.

......, in contradiction with Lemma 2.

This is a clear contradiction of the fact that ......

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