
theorem
  for A, B being RelStr, C being non empty RelStr for f, g being
Function of [:A,B:],C st for x being Element of A, y being Element of B holds f
  .(x,y) = g.(x,y) holds f = g
proof
  let A, B be RelStr, C be non empty RelStr, f, g be Function of [:A,B:],C;
  assume
  for x being Element of A, y being Element of B holds f.(x,y) = g.(x, y);
  then
A1: for x, y being set st x in the carrier of A & y in the carrier of B
  holds f.(x,y) = g.(x,y);
  the carrier of [:A,B:] = [:the carrier of A,the carrier of B:] by Def2;
  hence thesis by A1,BINOP_1:1;
end;
