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Proof step 52 from proof lift-unknown (previous step)

rs1 ∩ rs0 = ∅, r =>_(mk(rs1, f)), R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ (r ==>_ * R)[rs1 ∪ rs0, f, g], r ==>_[rs1, f, g]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information