How did leading american thinkers justify america's westward expansion in the 19th century?

Monroe Doctrine: It is the conception of foreign policy of the United States according to which any attempt of colonization or intervention of a European power in the territory of the American continent will be answered by the United States, which will not tolerate any kind of interference in the area. To this doctrine he is also known with the expression of America for the Americans.

On the other hand we also have the Doctrine of manifest destiny

The manifest destiny consists of a series of ideas that justified the expansion towards the West. These were:

The government of the United States, the Constitution and the institutions of the country and, as a result, the Americans themselves, have virtues that make them unique and special.

As a consequence of the foregoing, Americans have a moral obligation to propagate their form of government and their vision of the world. And that in this mission they will be accompanied by God.

either wyoming or idaho

could you go a bit more in depth with you question? it's quite hard to understand. as soon as you do that i will be glad to : )