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Proof step 5 from proof union-eq-rem-subseteq (previous step)

union(asar, 0, # asar) = as -- adr, n < # asar ⊦ ∀ adr. adr ∈ asar[n] → adr ∈ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
union(asar, 0, # asar) = as -- adr, n < # asar, adr0 ∈ asar[n] ⊦ # asar[n] = 0, asar[n] = ∅, adr0 ∈ as

Rule argument

Additional information

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