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Proof step 8 from proof sep (previous step)

mk(rs, f) = H0 ∪ H, P0(H0), P1(H), H0 ⊥ H, ∃ rs, f. H0 = mk(rs, f) ⊦ ∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ P0(mk(rs0, f)) ∧ P1(mk(rs1, f))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information