You have not cast a spell using Demon of Fate's Design's ability this turn.
Creatures you control excluding Trostani have total base toughness 7 or greater.
Steps
Cast Day of the Dragons by paying 7 life due to Demon of Fate's Design.
When Day of the Dragons enters the battlefield, its first ability and Cloudstone Curio trigger.
Resolve the Cloudstone Curio trigger, returning nothing to your hand from the battlefield.
Resolve the Day of the Dragons trigger, exiling all creatures you control and creating that many 5/5 Dragon creature tokens.
When the Dragon(s) enter the battlefield, Cloudstone Curio triggers that many times.
Resolve all but one Cloudstone Curio trigger, returning nothing to your hand from the battlefield.
Resolve the final Cloudstone Curio trigger, returning Day of the Dragons to your hand from the battlefield.
When Day of the Dragons leaves the battlefield, its second ability triggers, causing you to sacrifice all Dragons you control and return all cards exiled with Day of the Dragons to the battlefield.
When the creatures that were exiled by Day of the Dragons enter the battlefield, Cloudstone Curio triggers that many times, and Trostani triggers for each creature except itself.
Resolve all Trostani triggers, causing you to gain life equal to the collective toughness of the other creatures that entered the battlefield.
Resolve all Cloudstone Curio triggers, returning nothing to your hand from the battlefield.
Repeat.
If creatures you control excluding Trostani have total base toughness 8 or greater, this combo nets infinite life.