reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem Th86:
  for C being CategorySet holds CatToSet SetToCat C = C
  proof
    let C be CategorySet;
    ex y1,y2 be set,y3,y4 be Function of y2,y1,
      y5 be PartFunc of [:y2,y2:],y2 st
      y1 = C`1 & y2 = C`2 & y3 = C`3 & y4 = C`4 & y5 = C`5 &
      SetToCat C = CatStr(# y1,y2,y3,y4,y5 #) by Def31;
    hence thesis;
  end;
