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Proof step 5 from proof prefixn-toset-inter-empty (previous step)

ax.toSet ∩ as = ∅ ⊦ #((n ≤ # ax ⊃ firstn(n, ax);ax).toSet ∩ as) = 0, (n ≤ # ax ⊃ firstn(n, ax);ax).toSet ∩ as = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
ax.toSet ∩ as = ∅ ⊦ #(firstn(n, ax).toSet ∩ as) = 0, firstn(n, ax).toSet ∩ as = ∅, (n ≤ # ax ⊃ firstn(n, ax);ax).toSet ∩ as = ∅

Rule argument

Additional information

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