INSTRUCTOR ARTCC CTLR ALLOWED TRAINEE CTLR TO CLB A REGIONAL JET TO FL290 WITH A B737 IN CRUISE AT FL280.

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WBOUND B737 AT FL280 WAS ONLY ACFT AT FL280 IN SECTOR. 13 TOTAL ACFT IN SECTOR. OJT WAS IN PROGRESS (I WAS TRAINING AN FPL WHO WAS CURRENT ON THE HIGH ALT PORTION OF THE SECTOR BUT WAS GETTING TRAINING TIME ON THE LOW ALT PORTION). DEP RUSH WAS OCCURRING FROM DENVER AND SEVERAL CONFLICTIONS NEEDED TO BE SOLVED ON ACFT AT BOTH FL310 AND FL330. REGIONAL JET FROM DEN-MEM DEPARTED REQUESTING FL330 WAS TOLD THAT FL290 WOULD BE A FINAL ALT DUE TO TFC. REGIONAL JET FILED DEN-PLAINS 2 GCK; WHICH WAS A STEEP SOUTHERN TURN. PLT REQUESTED DIRECT ROUTING. TRAINEE RESPONDED THAT HE HAD HIS REQUEST. AFTER REGIONAL JET MADE THE SOUTHERN TURN TOWARD GCK (PUTTING ACFT IN CONFLICT WITH B737); TRAINEE ISSUED DIRECT MEM TO REGIONAL JET. DIRECT ROUTING WAS NOT ENOUGH TO SEPARATE ACFT. I POINTED OUT THE CONFLICT TO TRAINEE WHO ISSUED A 40 DEG L TURN TO REGIONAL JET. TRAINEE ISSUED A 40 DEG L TURN ALSO TO B737; WHO HESITATED; THEN RESPONDED THAT HE HAD AN RA AND WAS DSNDING. TRAINEE TOLD REGIONAL JET TO EXPEDITE CLB. I DID NOT STAND BEHIND TRAINEE; BUT WAS SEATED BESIDE HIM OFFERING SUGGESTIONS FOR SEPARATION OF ACFT BY DIVERGING RTES. ACFT AT FL280 WAS 'INVISIBLE;' SURROUNDED BY ACFT AT FL310.