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Proof step 26 from proof ex-shift-o (previous step)

P(H0), oP(o)(H1), H1 ⊥ H0, ∀ r. r ∈ H1 → O(r) = me ⊦ ((!(me, O, _∃ oP) * P))(H1 ∪ H0), (_∃ oP)(H1) ∧ (∀ r. r ∈ H1 → O(r) = me)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
P(H0), oP(o)(H1), H1 ⊥ H0, ∀ r. r ∈ H1 → O(r) = me ⊦ ((!(me, O, _∃ oP) * P))(H1 ∪ H0), ∃ o. oP(o)(H1)

Rule argument

Additional information

Used simplifier rules: ⊦ (_∃ oP)(H) ↔ (∃ o. oP(o)(H)); (s)