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

theorem Th87:
  for C being strict Category holds SetToCat CatToSet C = C
  proof
    let C be strict Category;
    set C2 = CatToSet C;
    ex  y1,y2 be set,y3,y4 be Function of y2,y1,
    y5 be PartFunc of [:y2,y2:],y2 st
    y1 = C2`1 & y2 = C2`2 & y3 = C2`3 & y4 = C2`4 & y5 = C2`5 &
    SetToCat C2 = CatStr(# y1,y2,y3,y4,y5 #) by Def31;
    hence thesis;
  end;
