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Proof step 9 from proof mapex-new (previous step)

P(H) ⊦ r = null, r ∈ H, ¬ r ∈ H ∧ H ++ r = (∅ ++ r)[r, (H ++ r)[r]] ∪ H ∧ P(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information