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Proof step 19 from proof write-known-p (previous step)

((r => o0 * P))(H0), P0(H), rely(me, O1, H0[r, o1] ∪ H, O2, H2), H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ !(me, O2, r => o1 * P)(H0[r, o1]), ((!(me, O2, r => o1 * P) * P0))(H0[r, o1] ∪ H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ !(id, O, P)(H) ↔ P(H) ∧ (∀ r. r ∈ H → O(r) = id)
Proof step 21:
((r => o0 * P))(H0), P0(H), rely(me, O1, H0[r, o1] ∪ H, O2, H2), H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ ((!(me, O2, r => o1 * P) * P0))(H0[r, o1] ∪ H), ((r => o1 * P))(H0[r, o1]) ∧ (∀ r0. r0 ∈ H0[r, o1] → O2(r0) = me)

Rule argument

spec: <toplevel> name: owned seq: ⊦ !(id, O, P)(H) ↔ P(H) ∧ (∀ r. r ∈ H → O(r) = id) subst: [H, P, O, id] → [H0[r, o1], r => o1 * P, O2, me] flags: <all paths>

Additional information

Used terms: H0[r, o1], r => o1 * P, O2, me