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

⊦ (∃ H0, H1, H2. H0 ⊥ H2 ∧ H0 ⊥ H1 ∧ H1 ⊥ H2 ∧ H = H0 ∪ H1 ∪ H2 ∧ P(H0 ∪ H2) ∧ emp(H1 ∪ H2)) ↔ P(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ (∃ H0, H1, H2. H0 ⊥ H2 ∧ H0 ⊥ H1 ∧ H1 ⊥ H2 ∧ H = H0 ∪ H1 ∪ H2 ∧ P(H0 ∪ H2) ∧ H1 ∪ H2 = ∅) ↔ P(H)

Rule argument

Additional information

Used simplifier rules: emp: ⊦ emp(H) ↔ H = ∅;