ACR X DSCNT TO OCCUPIED ALT HAD LTSS FROM ACR Y. SYS ERROR.

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ACR Y AT FL240; ACR X DSNDED TO FL250 INITIALLY. ACR X MISSED THE 1ST CLRNC. WHEN ACR X WAS CLRED AGAIN; IT WAS TO FL240. FEDERAL SEPARATION WAS LOST. TFC AT THE RADAR SECTOR DURING THIS TIME WAS MODERATE TO HVY. SUPPLEMENTAL INFO FROM ACN 234248: 2 ACFT INBOUND TO DTW; 1 AT FL240; THE OTHER FL310 DSNDING TO FL250. RADAR TRAINING WAS BEING CONDUCTED. WHEN TRAINEE ISSUED THE CLRNC TO DSND TO FL250; ACR X SAID BLOCKED CLRNC REISSUED TO FL240. THIS TIME NO ONE CAUGHT READBACK ERROR. TFC WAS HVY; MODERATE AT TIME OF ERROR. SUPPLEMENTAL INFO FROM ACN 234118: ACR X AT FL280 AND INDICATING 335 KTS SINCE ZID TOLD US TO MAINTAIN BEST FORWARD AIRSPD SO HE COULD GET US IN FRONT OF ACR Y THAT WAS ALSO GOING TO DTW. WE WERE THEN CLRED TO DSND TO FL240. WE SAW AN ACFT BELOW US IN FRONT AND JUST GOING UNDER OUR NOSE ON THE SAME FLT PATH. I QUESTIONED THE CTLR ABOUT THE ALT OF THE ACFT BELOW US AND HE SAID THAT HE WAS AT FL240 AND THAT THAT WAS ACR X THAT HE WAS PUTTING US IN FRONT OF. WE MENTIONED TO EACH OTHER THAT IT SEEMED STRANGE FOR CTR TO CLR US TO FL240 WHEN ACR Y BELOW US WAS AT FL240 BUT AS WE DSNDED WE WATCHED HIM FALL BEHIND US ON THE TCASII. BY THE TIME WE LEVELED OFF AT FL240 THE TCASII SHOWED ACR Y AT 1.8 MI BEHIND US AND FALLING BACK QUICKLY. SOON AFTER THAT; ZID ASKED US WHAT ALT WE WERE AT AND I REPLIED 'FL240.' HE SAID THAT WE WERE ONLY CLRED TO FL250. I SAID THAT WE BOTH HEARD THE CLRNC TO FL240 BUT WE WOULD CLB BACK UP TO FL250. HE SAID NO; MAINTAIN FL240 NOW. I SHOULD HAVE CONFIRMED THE ALT WITH THE CTLR SINCE WE THOUGHT IT WAS STRANGE; BUT WE WERE WATCHING ACR Y ON THE TCASII ALL THE WAY DOWN AND SAW THAT IT WASN'T A CONFLICT.