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Proof step 2 from proof delswr (previous step)

r ∈ rs, r ∈ H ⊦ H[r, o] \ rs = H \ rs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
r ∈ rs, r ∈ H ⊦ # rs = 0, H[r, o] \ rs = H \ rs, rs = ∅

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ rs ≠ ∅ → # rs ≠ 0; (forward) from specification set-basic[refset]%ne-01: ⊦ r ∈ rs → rs ≠ ∅; (forward) from specification set-basic[refset]