reserve i,j,k,n for Nat;
reserve x,x1,x2,x3,y1,y2,y3 for set;

theorem Th16:
  for S,R being RelStr holds S,R are_isomorphic implies card the
  InternalRel of S = card the InternalRel of R
proof
  let S,R be RelStr;
  assume
A1: S,R are_isomorphic;
  then
A2: ex f being Function of S,R st f is isomorphic;
  per cases by A2,WAYBEL_0:def 38;
  suppose
    S is non empty & R is non empty;
    hence thesis by A1,Lm1;
  end;
  suppose
    S is empty & R is empty;
    then reconsider S, R as empty RelStr;
    the InternalRel of S = {} & the InternalRel of R = {};
    hence thesis;
  end;
end;
