reserve X for non empty UNITSTR;
reserve a, b for Real;
reserve x, y for Point of X;
reserve X for RealUnitarySpace;
reserve x, y, z, u, v for Point of X;

theorem
  (a*x) .|. y = x .|. (a*y)
proof
  (a*x) .|. y = a * x .|. y by Def2;
  hence thesis by Def2;
end;
