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Proof step 4 from proof introduce-sharing (previous step)

∃ H0, H1, H2. H0 ⊥ H2 ∧ H0 ⊥ H1 ∧ H1 ⊥ H2 ∧ H = H0 ∪ H1 ∪ H2 ∧ P0(H0 ∪ H2) ∧ P1(H1 ∪ H2) ⊦ ∃ P. (((P -* P0) * (P -* P1) * P))(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information