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Proof step 52 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 22:
(!(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

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]