reserve A,B,C for Ordinal,
  X,X1,Y,Y1,Z for set,a,b,b1,b2,x,y,z for object,
  R for Relation,
  f,g,h for Function,
  k,m,n for Nat;
reserve M,N for Cardinal;

theorem Th1:
  M,N are_equipotent implies M = N
proof
A1: ex A st M = A & for C st C,A are_equipotent holds A c= C by Def1;
  ex B st N = B & for C st C,B are_equipotent holds B c= C by Def1;
  hence thesis by A1;
end;
