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Proof step 2 from proof range-inter-empty-in (previous step)

as ∩ range ri = ∅, ri[key] ∈ as, key ∈ ri ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
as ∩ range ri = ∅, ri[key] ∈ as, key ∈ ri ⊦ # as = 0, as = ∅

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]