Quick Double Strike question

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Mirran Crusader enchanted with Lifelink. It attacks and is blocked by a Doomed Traveler.

Does the Mirran Crusader's controller gain 4 life or 2?
2
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2.

It will deal 2 damage to Doomed Traveler during the first strike part of combat, you will gain 2 life and the Traveler will die and put a spirit into play.

Then you won't deal any damage in the regular combat step since the blocker is already dead.
This is probably a dumb question, sorry.

Mirran Crusader enchanted with Lifelink. It attacks and is blocked by a Doomed Traveler.

Does the Mirran Crusader's controller gain 4 life or 2?



two.

In the first combat damage step, the Crusader deals 2 damage and the controller gains 2 life.  In the second combat damage step, the Crusader is still blocked, but there is no blocking creature, so it deals no damage.

If the Crusader had Trample, it would deal 2 damage to the player in the second combat damage step, gaining its controller 2 more life.
 
Thanks folks.
My friend is disputing this ruling citing this from the Comprehensive Rulebook:

"511.3. As soon as the end of combat step ends, all creatures and planeswalkers are removed from
combat. After the end of combat step ends, the combat phase is over and the postcombat main phase
begins (see rule 505).

After first strike is completed, the game does not progress to the end combat step and begin a new combat step.  Instead it proceeds to a second phase wherein creatures have not yet been removed.
Rule for First Strike/Double Strike
702.7b If at least one attacking or blocking creature has first strike or double strike (see rule 702.4)
as the combat damage step begins, the only creatures that assign combat damage in that step are
those with first strike or double strike. After that step, instead of proceeding to the end of
combat step, the phase gets a second combat damage step. The only creatures that assign combat
damage in that step are the remaining attackers and blockers that had neither first strike nor
double strike as the first combat damage step began, as well as the remaining attackers and
blockers that currently have double strike. After that step, the phase proceeds to the end of
combat step."

He believes that the creature, in this case the Traveler, is not removed from combat after the first strike/double strike combat damage step. He beleives that Travelever is only removed from combat at the very end of combat.

Would someone mind helping me find a ruling to better explain this to him? I basically have to have something along those lines or he won't believe me. I know it has to do with a creature having lethal damage on it and that creature going to the GY as a state based action but I'm having trouble finding proof.
He's incorrect. 

The traveller will be removed from combat when it dies during the first strike combat damage step.


506.4. A permanent is removed from combat if it leaves the battlefield, if its controller changes, if it phases out, if an effect specifically removes it from combat, if it’s a planeswalker that’s being attacked and stops being a planeswalker, or if it’s an attacking or blocking creature that regenerates (see rule 701.12) or stops being a creature. A creature that’s removed from combat stops being an attacking, blocking, blocked, and/or unblocked creature. A planeswalker that’s removed from combat stops being attacked.


704. State-Based Actions

704.3. Whenever a player would get priority (see rule 116, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event. If any state-based actions are performed as a result of a check, the check is repeated; otherwise all triggered abilities that are waiting to be put on the stack are put on the stack, then the check is repeated. Once no more state-based actions have been performed as the result of a check and no triggered abilities are waiting to be put on the stack, the appropriate player gets priority. This process also occurs during the cleanup step (see rule 514), except that if no state-based actions are performed as the result of the step’s first check and no triggered abilities are waiting to be put on the stack, then no player gets priority and the step ends.

704.5g If a creature has toughness greater than 0, and the total damage marked on it is greater than or equal to its toughness, that creature has been dealt lethal damage and is destroyed. Regeneration can replace this event.



 


 




All Generalizations are Bad
My friend is disputing this ruling citing this from the Comprehensive Rulebook:

"511.3. As soon as the end of combat step ends, all creatures and planeswalkers are removed from
combat. After the end of combat step ends, the combat phase is over and the postcombat main phase
begins (see rule 505).

After first strike is completed, the game does not progress to the end combat step and begin a new combat step.  Instead it proceeds to a second phase wherein creatures have not yet been removed.
Rule for First Strike/Double Strike
702.7b If at least one attacking or blocking creature has first strike or double strike (see rule 702.4)
as the combat damage step begins, the only creatures that assign combat damage in that step are
those with first strike or double strike. After that step, instead of proceeding to the end of
combat step, the phase gets a second combat damage step. The only creatures that assign combat
damage in that step are the remaining attackers and blockers that had neither first strike nor
double strike as the first combat damage step began, as well as the remaining attackers and
blockers that currently have double strike. After that step, the phase proceeds to the end of
combat step."

He believes that the creature, in this case the Traveler, is not removed from combat after the first strike/double strike combat damage step. He beleives that Travelever is only removed from combat at the very end of combat.

Would someone mind helping me find a ruling to better explain this to him? I basically have to have something along those lines or he won't believe me. I know it has to do with a creature having lethal damage on it and that creature going to the GY as a state based action but I'm having trouble finding proof.

...so are you guys still friends?
The process of removing creatures from combat at the end of the combat phase is only necessary for creatures that are still around at the end of the battle. There are plenty of other ways to remove something from combat, and a creature dying or otherwise leaving the battlefield is one of the most common. There are also spells and abilities that can simply remove a creature because they say so, such as the side-effects of regeneration or the "Gustcloak" ability (can't remember exact card name). Removing them from combat as combat ends is just tying up loose ends.
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The final piece of the puzzle. SBA's will check between 510.3 and 510.4 and send the lethally damaged creature to the yard before the next combat damage step starts per 510.5
510.2. Second, all combat damage that‘s been assigned is dealt simultaneously. This turn-based action doesn‘t use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it‘s dealt. This is a change from previous rules.

510.3. Third, any abilities that triggered on damage being assigned or dealt go on the stack.

510.4. Fourth, the active player gets priority. Players may cast spells and activate abilities.

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