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Proof step 12 from proof propagate (previous step)

!(me, O2, P)(H0), ((!(id, O2, P1) * true))(H0 ∪ H1), P0(H), rely(me, O1, H0 ∪ H, O2, H0 ∪ H1), H0 ⊥ H, H1 ⊥ H0 ⊦ id = me, ((!(me, O2, P) * !(id, O2, P1) * true))(H0 ∪ H1), !(me, O2, P)(H0) ∧ ((!(id, O2, P1) * true))(H1) ∧ H0 ⊥ H1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
!(me, O2, P)(H0), ((!(id, O2, P1) * true))(H0 ∪ H1), P0(H), rely(me, O1, H0 ∪ H, O2, H0 ∪ H1), H1 ⊥ H0, H0 ⊥ H ⊦ id = me, ((!(me, O2, P) * !(id, O2, P1) * true))(H0 ∪ H1), ((!(id, O2, P1) * true))(H1)

Rule argument

Additional information

Used simplifier rules: ⊦ H0 ⊥ H1 → H1 ⊥ H0; (s)