Electrons and positrons have been smashed together before. It has been done at CERN before, too. The premise of this experiment is to do it at higher energy than has been done before.
The scientific goals of that experiment are somewhat more unclear, though. The LHC had a landmark scientific purpose, finding the last particle in the standard model. There is, as far as I can tell, no specific experiment that can be the headline for this new machine because the LHC pretty much did its job (modulo some error) and string theory et al need higher energy. There are a bunch of guesses about the higgs field and about dark matter that failed to materialize at the LHC, so now we want moar energy to see if that fixes our problems.
As to the theory they will be proving, maybe there are a few minor ones about the higgs field, but that's pretty much it at this point.
The scientific goals of that experiment are somewhat more unclear, though. The LHC had a landmark scientific purpose, finding the last particle in the standard model. There is, as far as I can tell, no specific experiment that can be the headline for this new machine because the LHC pretty much did its job (modulo some error) and string theory et al need higher energy. There are a bunch of guesses about the higgs field and about dark matter that failed to materialize at the LHC, so now we want moar energy to see if that fixes our problems.
As to the theory they will be proving, maybe there are a few minor ones about the higgs field, but that's pretty much it at this point.