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Proof step 40 from proof introduce-sharing (previous step)

P(H), P0(H ∪ H1), P1(H ∪ H2), H1 ⊥ H, H1 ⊥ H2, H2 ⊥ H ⊦ ∃ H0, H3, H4. H0 ⊥ H4 ∧ H0 ⊥ H3 ∧ H3 ⊥ H4 ∧ H1 ∪ H2 ∪ H = H0 ∪ H3 ∪ H4 ∧ P0(H0 ∪ H4) ∧ P1(H3 ∪ H4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ H0 ⊥ H1 → H1 ∪ H0 = H0 ∪ H1
Proof step 42:
P(H), P0(H ∪ H1), P1(H2 ∪ H), H1 ⊥ H2, H1 ⊥ H, H2 ⊥ H ⊦ ∃ H0, H3, H4. H0 ⊥ H4 ∧ H0 ⊥ H3 ∧ H3 ⊥ H4 ∧ H1 ∪ H2 ∪ H = H0 ∪ H3 ∪ H4 ∧ P0(H0 ∪ H4) ∧ P1(H3 ∪ H4)

Rule argument

spec: heap name: uni-com seq: ⊦ H0 ⊥ H1 → H1 ∪ H0 = H0 ∪ H1 subst: [H0, H1] → [H2, H] flags: <all paths>

Additional information

Used terms: H2, H