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Proof step 5 from proof range-inter-empty-in (previous step)

key ∈ ri, ri[key] ∈ as, ∀ adr. adr ∈ as ∩ range ri ↔ adr ∈ ∅ ⊦ # as = 0, as = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
ri[key] ∈ as, key ∈ ri, ∀ adr. ¬ adr ∈ as ∩ range ri ⊦ # as = 0, as = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ ∅; (s)