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Proof step 33 from proof write-known-p (previous step)

H1[r, o1] = H0 ∪ H, ((r => o1 * P))(H0), P0(H), rely(me, O1, H1[r, o1], O2, H2), r ∈ H1, H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ ((!(me, O2, r => H1[r] * P) * P0))(H1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1))
Proof step 35:
H1[r, o1] = H0 ∪ H, ((r => o1 * P))(H0), P0(H), rely(me, O1, H1[r, o1], O2, H2), r ∈ H1, H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ ∃ H0, H2. H0 ⊥ H2 ∧ H1 = H0 ∪ H2 ∧ !(me, O2, r => H1[r] * P)(H0) ∧ P0(H2)

Rule argument

spec: heap-sep name: sep seq: ⊦ ((P0 * P1))(H) ↔ (∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1)) subst: [H, P1, P0] → [H1, P0, !(me, O2, r => H1[r] * P)] flags: <all paths>

Additional information

Used terms: H1, P0, !(me, O2, r => H1[r] * P)