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Proof step 7 from proof alloc-p (previous step)

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

User applied rule apply lemma

And obtained the following new goals

Proof step 8:
⊦ r =>_ = !(me, O(r; me), r =>_)
Proof step 9:
r =>_ = !(me, O1(r; me), r =>_), ((r =>_ * !(me, O1, P) * P0))(H1 ++ r), ((!(me, O1, P) * P0))(H1), rely(me, O1(r; me), H1 ++ r, O2, H2) ⊦ r = null, ((!(me, O2, r =>_ * P) * P0))(H1 ++ r), r ∈ H1

Rule argument

spec: <toplevel> name: lift-mapex seq: ⊦ r =>_ = !(me, O(r; me), r =>_) subst: [r, me, O] → [r, me, O1]

Additional information

Used terms: r, me, O1