[to sth; see also: otherwise, contradiction
Suppose that, contrary to our claim,......
We now show that A is closed. Suppose that, on the contrary, there is an x......
In the contrary case,......
There is no evidence to the contrary.
Hence F is bounded, contrary to assumption.
[Do not write: “Contrary to [5], our example is finite-dimensional'' if you mean: In contrast to [5], our example is finite-dimensional.]