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Proof step 3 from proof write-known-p (previous step)

rely(me, O1, H1[r, o1], O2, H2) ⊦ ((!(me, O2, r => o0 * P) * P0))(H1) ↔ ((!(me, O2, r => o1 * P) * P0))(H1[r, o1]) ∧ H1[r] = o0 ∧ r ∈ H1

User applied rule case distinction

And obtained the following new goals

Proof step 4:
((!(me, O2, r => o0 * P) * P0))(H1), rely(me, O1, H1[r, o1], O2, H2) ⊦ ((!(me, O2, r => o1 * P) * P0))(H1[r, o1]) ∧ H1[r] = o0 ∧ r ∈ H1
Proof step 26:
H1[r] = o0, ((!(me, O2, r => o1 * P) * P0))(H1[r, o1]), rely(me, O1, H1[r, o1], O2, H2), r ∈ H1 ⊦ ((!(me, O2, r => o0 * P) * P0))(H1)

Rule argument

pos: right 1

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