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Proof step 18 from proof write-known-p (previous step)

((r => o0 * P))(H0), P0(H), rely(me, O1, H0[r, o1] ∪ H, O2, H2), H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ ((!(me, O2, r => o1 * P) * P0))(H0[r, o1] ∪ H), !(me, O2, r => o1 * P)(H0[r, o1]) ∧ (∀ r0. ¬ r0 ∈ H0[r, o1] ∨ ¬ r0 ∈ H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
((r => o0 * P))(H0), P0(H), rely(me, O1, H0[r, o1] ∪ H, O2, H2), H0 ⊥ H, ∀ r. r ∈ H0 → O2(r) = me ⊦ !(me, O2, r => o1 * P)(H0[r, o1]), ((!(me, O2, r => o1 * P) * P0))(H0[r, o1] ∪ H)

Rule argument

Additional information

Used simplifier rules: ⊦ r ∈ H1 ∧ H0 ⊥ H1 → (r ∈ H0 ↔ false); (s)% ⊦ r ∈ H[r0, o] ↔ r ∈ H; (s)