reserve V,X,Y for RealLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve a for Real;
reserve V1,V2,V3 for Subset of V;
reserve x for object;
reserve W,W1,W2 for Subspace of V;
reserve w,w1,w2 for VECTOR of W;

theorem Th15:
  w = v implies - v = - w
proof
A1: - v = (- jj) * v & - w = (- jj) * w by RLVECT_1:16;
  assume w = v;
  hence thesis by A1,Th14;
end;
