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Proof step 16 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) * P0))(H0[r, o1] ∪ H), !(me, O2, r => o1 * P)(H0[r, o1]) ∧ H0[r, o1] ⊥ H

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ H0 ⊥ H1 ↔ (∀ r. ¬ r ∈ H0 ∨ ¬ r ∈ H1)
Proof step 18:
((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), !(me, O2, r => o1 * P)(H0[r, o1]) ∧ (∀ r0. ¬ r0 ∈ H0[r, o1] ∨ ¬ r0 ∈ H)

Rule argument

spec: heap name: disj seq: ⊦ H0 ⊥ H1 ↔ (∀ r. ¬ r ∈ H0 ∨ ¬ r ∈ H1) subst: [H1, H0] → [H, H0[r, o1]] flags: <all paths>

Additional information

Used terms: H, H0[r, o1]