BOO question- sorry if this is a repeat

[DUNDALKCHOPPER]

This question was asked elsewhere but I did not see an answer. WHO starts the next inning ??? Alice or Fred
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Rule change for ASA.

Rule 7 Section 2D [2]: If batting out of order is discovered after the incorrect batter has completed a turn at bat:
a. The improper batter’s time at bat is negated.
b. The player who should have batted is out.
c. Any advancement or score of a runner as a result of the improper batter is negated. Runners not called out must return to the last base occupied at the time of the pitch. Any runner, who is called out prior to the discovery of the infraction, remains out
d. The next batter is the player whose name follows that of the player called out for failing to bat.
EXCEPTION: (Co-ed Only) If the incorrect batter is called out as a result of their time at bat, and is scheduled to be the proper batter, skip that player and the next person in the line-up will be the batter.
Comment: Rewords the rule so if the Batter-Runner is called out that out applies to the batter who should have batted. All outs made by runners are still out. If the incorrect batter makes an out and is the next legal batter they simply bat again. The old rule of all outs stand including the batter runner and skipping the batter if they make an out and they are the next legal batter, still applies to the game of Co-ed.

If your line up is as follows:
1: John
2: Mary
3: Mike
4: Alice
5: Fred
6: Ann

Mary bats and gets to 1st base.
Mike is due up to bat but Alice gets up and hits into a double play.
The defence appeal batting out of order
Mary is still out for the double play. Alice is out but the out is recorded as being Mike.


The Co-ed exception says that if the incorrect batter is called out as a result of their time at bat and is scheduled to be the next batter they are skipped and the next batter takes up the bat.


So in my example Mary is out in the double play, Alice is out in the double play and then Mike is out for the batting out of order. End of the half and Fred is the batter due up????????

Am I getting this wrong?