"suppost that" is the same as "assume that" -- both advance a supposition/hypothesis

"lemma" in mathematics is small but proven supposition used as a stepping stone in proving more complex supposition/theory. "lemma" is not an "incidental" or "addenda" (บทแทรก) but a "component" part of a whole (proof).

"clearly" (note a little "l" before "y").

Please edit your post to make mathematics clear and simple to learn.