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Proof step 7 from proof write-known-p (previous step)

!(me, O2, r => o0 * P)(H0), P0(H), rely(me, O1, (H0 ∪ H)[r, o1], O2, H2), H0 ⊥ H ⊦ ((!(me, O2, r => o1 * P) * P0))((H0 ∪ H)[r, o1]) ∧ (r ∈ H0 ⊃ H0[r];H[r]) = o0 ∧ (r ∈ H0 ∨ r ∈ H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ !(id, O, P)(H) ↔ P(H) ∧ (∀ r. r ∈ H → O(r) = id)
Proof step 9:
((r => o0 * P))(H0), P0(H), rely(me, O1, (H0 ∪ H)[r, o1], O2, H2), H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ ((!(me, O2, r => o1 * P) * P0))((H0 ∪ H)[r, o1]) ∧ (r ∈ H0 ⊃ H0[r];H[r]) = o0 ∧ (r ∈ H0 ∨ r ∈ H)

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 => o0 * P, O2, me] flags: <all paths>

Additional information

Used terms: H0, r => o0 * P, O2, me