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Proof step 43 from proof alloc-p (previous step)

(((!(me, O2, r =>_) * !(me, O2, P)) * P0))(H1 ++ r), rely(me, O1(r; me), H1 ++ r, O2, H2) ⊦ r = null, ((!(me, O1, P) * P0))(H1), r ∈ H1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ (P0 * P1) * P2 = P0 * P1 * P2
Proof step 45:
((!(me, O2, r =>_) * !(me, O2, P) * P0))(H1 ++ r), rely(me, O1(r; me), H1 ++ r, O2, H2) ⊦ r = null, ((!(me, O1, P) * P0))(H1), r ∈ H1

Rule argument

spec: heap-sep name: sep-ass seq: ⊦ (P0 * P1) * P2 = P0 * P1 * P2 subst: [P2, P1, P0] → [P0, !(me, O2, P), !(me, O2, r =>_)] flags: <all paths>

Additional information

Used terms: P0, !(me, O2, P), !(me, O2, r =>_)