theorem Th6:
  w is_atlas_of S,G implies for b,x ex a st w.(a,b) = x
proof
  assume
A1: w is_atlas_of S,G;
  let b,x;
  consider a such that
A2: w.(b,a) = -x by A1;
  take a;
  w.(a,b) = -(-x) by A1,A2,Th4
    .= x by RLVECT_1:17;
  hence thesis;
end;
