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Proof step 13 from proof rmpos-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
x0[n - 1] ∈ (x0[n - 1] ' + x0) -p n, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ n = 0, x0 = [], dups(x0), x0[n - 1] ∈ x0

Rule argument

Additional information

Used simplifier rules: ⊦ m < 1 ↔ m = 0; (s)% ⊦ # a ' = 0 +1; (s)