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Proof step 2 from proof rmpos-in (previous step)

n < # x ⊦ a ∈ x -p n ↔ a ≠ x[n] ∧ a ∈ x, dups(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < # x ⊦ a ∈ x -p n ↔ a ≠ x[n] ∧ a ∈ x, x = [], dups(x)

Rule argument

Additional information

Used simplifier rules: ⊦ # x = 0 ↔ x = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic