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Proof step 45 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 ∈ H0, r ∈ H1, H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ H1 = H1[r, o1][r, H1[r]]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
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 ⊦ H1 = H1[r, H1[r]]

Rule argument

Additional information

Used simplifier rules: ⊦ ((r => o * P))(H) → r ∈ H; (s)%sep-com: ⊦ P0 * P1 = P1 * P0; from specification heap-sep%sep-ass: ⊦ (P0 * P1) * P2 = P0 * P1 * P2; from specification heap-sep% ⊦ H[r, o0][r, o1] = H[r, o1]; (s)