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Proof step 8 from proof lift-unknown (previous step)

∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ r ==>(o, a)[rs0, f, g] ∧ R[rs1, f, g] ⊦ (a[r =>_] * R)[rs, f, g]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information