The aims of the two sides thus clashed hopelessly.

Under all temporary and apparent grounds of quarrel lay this deep-rooted jealousy and incompatibility of interests.

Beyond the Alleghanies the Revolution was fundamentally a struggle between England, bent on restricting the growth of the English race, and the Americans, triumphantly determined to acquire the right to conquer the continent.
The West Actually Conquered.
Had not the backwoodsmen been successful in the various phases of the struggle, we would certainly have been cooped up between the sea and the mountains.

If in 1774 and '76 they had been beaten by the Ohio tribes and the Cherokees, the border ravaged, and the settlements stopped or forced back as during what the colonists called Braddock's War, [Footnote: During this Indian war, covering the period from Braddock's to Grant's defeats, Smith, a good authority, estimates that the frontiers were laid waste, and population driven back, over an area nearly three hundred miles long by thirty broad.] there is every reason to believe that the Alleghanies would have become our western frontier.
Similarly, if Clark had failed in his efforts to conquer and hold the Illinois and Vincennes, it is overwhelmingly probable that the Ohio would have been the boundary between the Americans and the British.
Before the Revolution began, in 1774, the British Parliament had, by the Quebec Act, declared the country between the Great Lakes and the Ohio to be part of Canada; and under the provisions of this act the British officers continued to do as they had already done--that is, to hold adverse possession of the land, scornfully heedless of the claims of the different colonies.

The country was _de facto_ part of Canada; the Americans tried to conquer it exactly as they tried to conquer the rest of Canada; the only difference was that Clark succeeded, whereas Arnold and Montgomery failed.
But only Definitely Secured by Diplomacy.
Of course the conquest by the backwoodsmen was by no means the sole cause of our acquisition of the west.