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Proof step 10 from proof nodups-rmposnodups (previous step)

a ∈ x0 -1l n1, ∀ n0. ¬ dups(x0 -1l n0) ⊦ dups(x0 -1l n1), a ∈ x0, dups(x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: rmpos-in seq: ⊦ ¬ dups(x) ∧ n < # x → (a ∈ x -1l n ↔ a ≠ x[n] ∧ a ∈ x) subst: [n, x, a] → [n1, x0, a] flags: rewrite, current

Additional information

Used simplifier rules: rmtoobigpos: ⊦ # x ≤ n → x -1l n = x;%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat Used terms: n1, x0, a