Wide Mt. Bike Tires vs. Thin Tires

For the sake of this discussion assume that all things are equal
regarding quality of parts. I have an inexpensive mt bike with the
standard fairly wide tires and am thinking of getting a new inexpensive
26 in. bike however this one has the very thin tires. The mt. bike
tires appear to be at least three times as wide and possibly 4. Since
there is much less friction associated with the thin tires and remember
all things considered equal can I assume that the same energy and
exertion that I put into pedaling the mt. bike will be at the very
least 2 or more times effective when pedaling the bike with the very
thin tires.