C172 WITH STUDENT AND INSTRUCTOR ABOARD HAVE NMAC WITH CIRRUS IN TRAFFIC PATTERN WHILE TOWER IS IN OPERATION.

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I WAS TEACHING MY STUDENT HIS FIRST LESSON IN THE PATTERN. THE CLASS D AIRSPACE WAS BUSY AT THIS TIME WITH MULTIPLE ACFT IN THE PATTERN/REJOINING. AFTER A DECREASE IN THE TFC; THE FEMALE CTLR HANDED OVER TO HER MALE COLLEAGUE. AFTER APPROX 2 MORE CIRCUITS MY STUDENT BOUNCED ON LNDG; AT WHICH TIME I TOOK CTL AND INITIATED A GAR. I WAS INSTRUCTED TO CONTINUE AND MAKE R TFC RPTING THE DOWNWIND; TO WHICH I REPLIED 'WILCO.' AT APPROX 700 FT ON THE EXTENDED CTRLINE; MY STUDENT INITIATED A R TURN TO XWIND. WHILST LOOKING OUT IN THE DIRECTION OF THE TURN; I SPOTTED THE OTHER ACFT AT VERY CLOSE PROX TO OUR ACFT. I DEFLECTED THE CTL COLUMN FULLY FORWARD IN EVASIVE ACTION; WITHOUT WHICH I BELIEVE A COLLISION WOULD HAVE OCCURRED. THE OTHER ACFT RPTED THAT I HAD JUST PASSED BELOW THEM AND LATER I CONFIRMED I WAS 'DEFINITELY VISUAL' WITH THE OTHER ACFT WHEN REQUESTING A FULL STOP LNDG. AT NO TIME WAS I GIVEN A TFC RPT BY THE CTLR REGARDING THE INCOMING TFC TO THE DOWNWIND. IF I WAS GIVEN THE INFO THE SIT WOULD HAVE BEEN AVERTED AS I WOULD HAVE BEEN LOOKING FOR THE INCOMING TFC. I AM NOT AWARE WHETHER THE OTHER ACFT WAS GIVEN A TFC RPT FOR US; HOWEVER; I WAS THE LOWER OF THE 2 ACFT; SO I HAD RIGHT-OF-WAY IN THIS SIT.