for a lemma involving temporal operators to be useful, its hypotheses should be "boxed", i.e. occur in the scope of an always operator. For example, you could state
LEMMA BoxImplies ==
ASSUME NEW TEMPORAL F, NEW TEMPORAL G,
F, (F => G)
and then use this lemma somewhere in a proof about temporal properties. For details, please see section 8.3 of . In practice, we never state lemmas of (propositional) temporal logic because the PTL decision procedure proves them automatically.
Also note that your proof only goes through only because "NEW Invariant" implicitly means "NEW CONSTANT Invariant", hence the formula Invariant' in steps <1>2 and <1>3 gets rewritten to Invariant, and these steps are therefore tautologies. It is certainly not what you had in mind.
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