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We treat the lattice sine-Gordon equation and two of its generalisedsymmetries as a compatible system. Elimination of shifts from the twosymmetries of the lattice sine-Gordon equation yields an integrable NLS-typesystem. An auto-B\"acklund transformation and a superposition formula for theNLS-type system is obtained by elimination of shifts from the latticesine-Gordon equation and its down-shifted version. We use the obtained formulaeto calculate a superposition of two and three elementary solutions.

The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System