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Proof step 10 from proof propagate (previous step)

!(me, O2, P)(H0), ((!(id, O2, P1) * true))(H0 ∪ H1), P0(H), rely(me, O1, H0 ∪ H, O2, H0 ∪ H1), H1 ⊥ H0, H0 ⊥ H ⊦ id = me, ((!(me, O2, P) * !(id, O2, P1) * true))(H0 ∪ H1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1)
Proof step 12:
!(me, O2, P)(H0), ((!(id, O2, P1) * true))(H0 ∪ H1), P0(H), rely(me, O1, H0 ∪ H, O2, H0 ∪ H1), H0 ⊥ H, H1 ⊥ H0 ⊦ id = me, ((!(me, O2, P) * !(id, O2, P1) * true))(H0 ∪ H1), !(me, O2, P)(H0) ∧ ((!(id, O2, P1) * true))(H1) ∧ H0 ⊥ H1

Rule argument

spec: heap-sep name: split-union seq: ⊦ P0(H0) ∧ P1(H1) ∧ H0 ⊥ H1 → ((P0 * P1))(H0 ∪ H1) subst: [H1, H0, P1, P0] → [H1, H0, !(id, O2, P1) * true, !(me, O2, P)] flags: <all paths>

Additional information

Used terms: H1, H0, !(id, O2, P1) * true, !(me, O2, P)