reserve x for set;
reserve a,b,c,d,e,r1,r2,r3,r4,r5,r6 for Real;
reserve V for RealLinearSpace;
reserve u,v,v1,v2,v3,w,w1,w2,w3 for VECTOR of V;
reserve W,W1,W2 for Subspace of V;

theorem
  v1 - w = v2 - w implies v1 = v2
proof
  assume v1 - w = v2 - w;
  then - (v1 - w) = w - v2 by RLVECT_1:33;
  then w - v1 = w - v2 by RLVECT_1:33;
  hence thesis by RLVECT_1:23;
end;
