reserve a, b for Real;
reserve RNS for RealNormSpace;
reserve x, y, z, g, g1, g2 for Point of RNS;

theorem Th10:
  ||.x - z.|| <= ||.x - y.|| + ||.y - z.||
proof
  x - z = x + (09(RNS) + (-z))
    .= x + (((-y) + y) + (-z)) by RLVECT_1:5
    .= x + ((-y) + (y + (-z))) by RLVECT_1:def 3
    .= (x - y) + (y - z) by RLVECT_1:def 3;
  hence thesis by Def1;
end;
