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

theorem Th1:
  (w-v)+(v-u) = w-u
proof
  thus (w-v)+(v-u) = w-(v-(v-u)) by RLVECT_1:29
    .= w-((v-v)+u) by RLVECT_1:29
    .= w-(0.V+u) by RLVECT_1:15
    .= w-u by RLVECT_1:4;
end;
