 Then for every finite subset \(\Delta\) of \(\Gamma\), one can construct a model on a transitive, conversely well-founded frame and a world in the model where all formulas of \(\Delta\) are true. So by modal soundness, GL does not prove \(\bot\) from \(\Delta\) for any finite \(\Delta \subseteq \Gamma\), and a fortiori GL does not prove \(\bot\) from \(\Gamma\), as any GL-proof is finite. On the other hand, it is easy to see that there is no model on a transitive, conversely well-founded frame where in any world, all formulas of \(\Gamma\) hold. Thus \(\bot\) follows semantically from \(\Gamma\), but is not provable from it in GL, contradicting the condition of strong completeness.