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Proof step 12 from proof sep-partial-mp (previous step)

P0(H2), P2(H0), H2 ⊥ H1, H0 ⊥ H2, H0 ⊥ H1, H2 ∪ H0 ⊥ H1 ∧ ((P0 * P2))(H2 ∪ H0) → P1((H2 ∪ H0) ∪ H1) ⊦ P1(H0 ∪ H2 ∪ H1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ H1 ⊥ H2 → (H1 ∪ H2 ⊥ H0 ↔ H0 ⊥ H1 ∧ H0 ⊥ H2)
Proof step 14:
P0(H2), P2(H0), H0 ⊥ H1, H0 ⊥ H2, H2 ⊥ H1, H2 ⊥ H0, (H1 ⊥ H2 ∧ H1 ⊥ H0) ∧ ((P0 * P2))(H2 ∪ H0) → P1((H2 ∪ H0) ∪ H1) ⊦ P1(H0 ∪ H2 ∪ H1)

Rule argument

spec: heap name: disj-distr-uni-com seq: ⊦ H1 ⊥ H2 → (H1 ∪ H2 ⊥ H0 ↔ H0 ⊥ H1 ∧ H0 ⊥ H2) subst: [H0, H2, H1] → [H1, H0, H2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ H0 ⊥ H1 → H1 ⊥ H0; (s) Used terms: H1, H0, H2