reserve MS for non empty MidStr;
reserve a, b for Element of MS;
reserve M for MidSp;
reserve a,b,c,d,a9,b9,c9,d9,x,y,x9 for Element of M;
reserve p,q,r,p9,q9 for Element of [:the carrier of M,the carrier of M:];
reserve u,v,w,u9,w9 for Vector of M;

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;
