Single engine aircraft have enough performance to take-off, if everything is working.
FAR 35 light (usually piston) twins accelerate to the point where they can safely stop, then go through a "grey area" where they can neither stop nor continue to fly with an engine failure.
Transport category aircraft (usually jets) accelerate to the point where they can safely stop on the runway, and after that point they have a guaranteed performance to fly with and engine failure - i.e. there is no grey area.
Now once the aircraft has reached Vr, it has by definition, enough performance to fly on one engine, so there is no need to abort from this point (we, and the regulators, are talking about engine failure here, not significant damage!). That is why V1 is never greater than Vr.
Note that once the aircraft has rotated, then the distance to stop is very technique dependant as it depends opon how long the pilot takes to put the aircraft back on the runway. Calculated V1s assume that the aircraft is in contact with the runway, and can begine braking immediately. If you were to go into the books, and work out a Vr of (say) 130 knots, and a V1 at the same weight of 135 knots, well once the wheels are off the deck that calculated V1 now has no meaning, as the basis for it (wheels on the deck) no longer applies.