theorem Th40:
  vect(a,b) + vect(b,c) = vect(a,c)
proof
  set p = [a,b], q = [b,c];
  set u = p~, v = q~;
  p`2 = b
    .= q`1;
  then q`2 = c & u + v = [p`1,q`2]~ by Def9;
  hence thesis;
end;
