theorem Th36:
  f is one-to-one implies dom(f*f") = rng f & rng(f*f") = rng f
proof
  assume
A1: f is one-to-one;
  then
A2: rng(f") = dom f by Th32;
  then dom(f*f") = dom(f") by RELAT_1:27;
  hence thesis by A1,A2,Th32,RELAT_1:28;
end;
