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Proof step 55 from proof lift-unknown (previous step)

rs1 ∩ rs0 = ∅, R[rs0, f, g], (_∃(λ o. r => o))(mk(rs1, f)), ∀ 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

Proof step 56:
rs1 ∩ rs0 = ∅, ((r => o))(mk(rs1, f)), R[rs0, f, g], ∀ r. r ∈ rs1 → g(r) = a ⊦ r ==>_[rs1, f, g], (r ==>_ * R)[rs1 ∪ rs0, f, g]

Rule argument

Additional information

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