reserve V for RealLinearSpace;
reserve p,q,u,v,w,y for VECTOR of V;
reserve a,b,c,d for Real;

theorem Th3:
  a*(u-v) = -(a*(v-u))
proof
  a*(v-u) + a*(u-v) = a*(v-u) + a*(-(v-u)) by RLVECT_1:33
    .= a*(v-u)-a*(v-u) by RLVECT_1:25
    .= 0.V by RLVECT_1:15;
  hence thesis by RLVECT_1:def 10;
end;
