Ummmm, those statements were all made during the campaign. Campaign rhetoric is often very very different from actual policy once the new president gets all the data. JFK for example ran on a platform of a big "missile gap" between the US and Soviet Union, which helped get him elected.. Once he got in office he learned there was no such gap and his actual policies were much different than his campaign rhetoric. Note that since winning the election Trump has talked a lot about nuclear supremacy and not at all about nuclear proliferation.
And Trump's proposed defense budget (the subject of this thread) has NOTHING to do with nuclear proliferation. Indeed it has very very little to do even with nuclear supremacy. In fact, the increase is actually quite modest, only about $19B above what Obama proposed. And to my knowledge, Obama is the only president who actively worked to proliferate nukes, explicitly allowing and financially assisting Iran to develop nukes.
As for increasing the number of warheads, Trump has said nothing of the sort since winning the election. Both Russia and the US have warhead caps and neither side has proposed increasing those caps.