Not really explained by the linked article, but my understanding is that as the Sun increases in luminosity (increasing the solar flux), the chemical reactions

Not really explained by the linked article, but my understanding is that as the Sun increases in luminosity (increasing the solar flux), the chemical reactions that binds CO2 will increase. Within 500-600 million years the CO2 levels drop beyond the point for C3 photosynthesis. Plants using C4 photosynthesis will survive for about twice as long, though by that point the increased solar flux will have caused the surface temperature on Earth to be uninhabitable anyways. Of course, who really knows how life might evolve to adapt to these changes. Humans have been pretty good at liberating carbon for instance :P.