theorem Th7:
  w is_atlas_of S,G & w.(b,a) = w.(c,a) implies b = c
proof
  assume that
A1: w is_atlas_of S,G and
A2: w.(b,a) = w.(c,a);
  w.(a,b) = w.(a,c) by A1,A2,Th5;
  hence thesis by A1;
end;
