reserve V for RealLinearSpace;
reserve u,u1,u2,v,v1,v2,w,w1,y for VECTOR of V;
reserve a,a1,a2,b,b1,b2,c1,c2 for Real;
reserve x,z for set;

theorem Th5:
  ex y st u#y=w
proof
  take y = (-u)+(w+w);
  u+y = (u+(-u))+(w+w) by RLVECT_1:def 3
    .= 0.V+(w+w) by RLVECT_1:5
    .= w+w by RLVECT_1:4;
  hence thesis by Def2;
end;
