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Proof step 9 from proof rmpos-in (previous step)

a = a0, a ∈ (a0 ' + x0) -1l n, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ x0 = [], a0 ∈ x0, dups(x0), a ≠ (a0 ' + x0)[n] ∧ (a = a0 ∨ a ∈ x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
a0 = (a0 ' + x0)[n], a0 ∈ (a0 ' + x0) -1l n, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ x0 = [], a0 ∈ x0, dups(x0)

Proof step 9 from proof rmpos-in (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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