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Proof step 16 from proof compact-local (previous step)

∀ r. r ∈ H → O(r) = me, ∃ H0, H1. H0 ⊥ H1 ∧ H = H0 ∪ H1 ∧ P0(H0) ∧ P1(H1) ⊦ ((!(me, O, P0) * !(me, O, P1)))(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
P0(H1), P1(H0), H1 ⊥ H0, ∀ r. r ∈ H1 ∨ r ∈ H0 → O(r) = me ⊦ ((!(me, O, P0) * !(me, O, P1)))(H1 ∪ H0)

Rule argument

Additional information

Used simplifier rules: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1); (s)