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Proof step 7 from proof pos-get (previous step)

n ≤ # x0, ∀ n0. n0 < # x0 → pos(x0[n0], x0) = n0 ∨ x0 = [] ⊦ pos(x0[n - # a '], a ' + x0) = n, n < # a ', dups(x0), a ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
n ≤ # x0, ∀ n0. n0 < # x0 → pos(x0[n0], x0) = n0 ∨ x0 = [] ⊦ n = 0, pos(x0[n - 1], a ' + x0) = n, dups(x0), a ∈ x0

Rule argument

Additional information

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