theorem Th22:
  vect(p,q) = vect(r,s) iff p@s = q@r
proof
  thus vect(p,q) = vect(r,s) implies p@s = q@r by MIDSP_1:37;
  thus p@s = q@r implies vect(p,q) = vect(r,s)
  proof
    assume p@s = q@r;
    then p,q @@ r,s by MIDSP_1:def 4;
    then [p,q] ## [r,s] by MIDSP_1:19;
    hence thesis by MIDSP_1:36;
  end;
end;
