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Proof step 2 from proof firstn-at-in-dups (previous step)

n < # x, x[n] ∈ firstn(n, x) ⊦ dups(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < # x, x[n] ∈ x, x[n] ∈ firstn(n, x) ⊦ x = [], dups(x)

Rule argument

Additional information

Used simplifier rules: firstN-in-05: ⊦ a ∈ firstn(n, x) ∧ n < # x → a ∈ x;% ⊦ # x = 0 ↔ x = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic