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

m ≤ # x0, ∀ m. m < # x0 → x0 = [] ∨ x0[m] ∈ x0 ⊦ a ' + x0 = [], (a ' + x0).tail[m - 1] = a, m = 0, (a ' + x0).tail[m - 1] ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
m ≤ # x0, ∀ m. m < # x0 → x0 = [] ∨ x0[m] ∈ x0 ⊦ x0[m - 1] = a, m = 0, x0[m - 1] ∈ x0

Rule argument

Additional information

Used simplifier rules: ⊦ a ' + x ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ (a ' + x).tail = x; (s)