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Proof step 19 from proof rmpos-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
n ≤ # x0, x0[n - 1] ∈ (a0 ' + x0) -1l n, x0[n - 1] ∈ x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ x0 = [], n = 0, dups(x0), a0 ∈ x0

Rule argument

Additional information

Used simplifier rules: one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%len-02: ⊦ # a ' = 0 +1; from specification list