This paper is an attempt to give an account of presupposition inheritance (henceforth PI) in conditionals from a functional-discourse perspective. The focus of study is on how to evaluate the embedded presupposition (EP) nested in the hypothetical world. I propose the view that if the EP satisfies the condition on the presupposition satisfaction, it becomes background information in the relevant world, arguing against the theories which employ simple cancellation or disappearance of those EPs. The discourse processing among discourse participants is to be considered in the light of functional significance for the explication of the contrastive mechanism of presupposition and assertion. I advance a revised model of PI in conditionals and analyze several problematic cases of conditionals, with a particular attention to their DRSs.