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Proof step 41 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 ⊦ H1 = H0[r, H1[r]] ∪ H ∧ !(me, O2, r => H1[r] * P)(H0[r, H1[r]])

User applied rule case distinction

And obtained the following new goals

Proof step 42:
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 = H0[r, H1[r]] ∪ H
Proof step 48:
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)(H0[r, H1[r]])

Rule argument

pos: right 1

Proof step 41 from proof write-known-p (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information