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Proof step 7 from proof propagate (previous step)

!(me, O2, P)(H0), ((!(id, O2, P1) * true))(H2), P0(H), rely(me, O1, H0 ∪ H, O2, H2), H0 ⊆ H2, H0 ⊥ H ⊦ id = me, ((!(me, O2, P) * !(id, O2, P1) * true))(H2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ H0 ⊆ H1 ↔ (∃ H. H0 ∪ H = H1 ∧ H ⊥ H0)
Proof step 9:
!(me, O2, P)(H0), ((!(id, O2, P1) * true))(H2), P0(H), rely(me, O1, H0 ∪ H, O2, H2), H0 ⊥ H, ∃ H. H0 ∪ H = H2 ∧ H ⊥ H0 ⊦ id = me, ((!(me, O2, P) * !(id, O2, P1) * true))(H2)

Rule argument

spec: heap name: subset-uni seq: ⊦ H0 ⊆ H1 ↔ (∃ H. H0 ∪ H = H1 ∧ H ⊥ H0) subst: [H1, H0] → [H2, H0] flags: <all paths>

Additional information

Used terms: H2, H0