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Proof step 16 from proof lift-emp (previous step)

∀ r. r ∈ rs → g(r) = a, ∀ r. (r ∈ mk(rs, f) ↔ r ∈ ∅) ∧ (r ∈ mk(rs, f) → mk(rs, f)[r] = (∅)[r]) ⊦ mk(rs, f, g) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
∀ r. r ∈ rs → g(r) = a, ∀ r. ¬ r ∈ rs ⊦ mk(rs, f, g) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ r ∈ ∅; (s)% ⊦ r ∈ mk(rs, f) ↔ r ∈ rs; (s)