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Proof step 18 from proof diffone-nodupsget (previous step)

n < # x0, a ∈ x0, n ≤ pos(a, x0), ∀ n0, a1. n0 + 1 < # x0 ∧ a1 ∈ x0 → (x0 \ a1 ')[n0] = (n0 < pos(a1, x0) ⊃ x0[n0];x0[n0 + 1]) ⊦ (x0 \ a ')[n - # a0 '] = (a0 ' + x0)[n], x0 = [], n < # a0 ', dups(x0), a0 ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
n < # x0, a ∈ x0, n ≤ pos(a, x0), ∀ n0, a1. n0 + 1 < # x0 ∧ a1 ∈ x0 → (x0 \ a1 ')[n0] = (n0 < pos(a1, x0) ⊃ x0[n0];x0[n0 + 1]) ⊦ (x0 \ a ')[n - 1] = x0[n - 1], n = 0, x0 = [], dups(x0), a0 ∈ x0

Rule argument

Additional information

Used simplifier rules: ⊦ m < 1 ↔ m = 0; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ ¬ n < # x → (x + y)[n] = y[n - # x]; (s)% ⊦ # a ' = 0 +1; (s)