reserve i,j,k for Nat;

theorem Th9:
  for i,j being Integer st i > 0 & j > 0 holds Euclid-Function.((
  dl.0,dl.1) --> (i,j)) = dl.0 .--> (i gcd j)
proof
  let i,j be Integer;
  assume i > 0 & j > 0;
  then [((a,b) --> (i,j)),a .--> (i gcd j)] in Euclid-Function by Def2;
  hence thesis by FUNCT_1:1;
end;
