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Proof step 2 from proof in-index-in-union (previous step)

n < m, adr ∈ asar[n] ⊦ adr ∈ union(asar, 0, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < m, adr ∈ asar[n] ⊦ # asar[n] = 0, asar[n] = ∅, adr ∈ union(asar, 0, m)

Rule argument

Additional information

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