1a entails 1b

1a. The leopard gecko ate the cricket.

1b. The cricket is dead.

 

2a presupposes 2b

2a. Jesse stopped playing Fortnite.

2b. Jesse once played Fortnite.

2a trigger; stopped.

3a presupposes 3b

3a. Togi used to be the best shaman in his clan.

3b. Togi is no longer the best shaman in his clan.

3a trigger; used to be.