Cita:
310.5. At the start of the combat damage step, if at least one attacking or blocking creature has first strike (see rule 502.2) or double strike (see rule 502.28), creatures without first strike or double strike don't assign combat damage. Instead of proceeding to end of combat, the phase gets a second combat damage step (see rule 310.1) to handle the remaining creatures. In the second combat damage step, any attackers and blockers that didn't assign combat damage in the first step, plus any creatures with double strike, assign their combat damage.
310.2c A blocked creature will assign combat damage, divided as its controller chooses, to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it will assign no combat damage.
A rigore di logica, in questo caso potresti paragonare il danno da first strike a un qualsiasi removal ([card]fulmine[/card]) sul bloccante.
Il tuo 2/2 DoubleStrike killa il suo 1/1 nella fase in cui parte il danno da first strike, ma nella fase del danno "normale", pur non avendo niente da danneggiare, conterà sempre come bloccata.
