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Proof step 6 from proof get-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m ≤ # x0, ∀ m. m < # x0 → x0 = [] ∨ x0[m] ∈ x0 ⊦ m = 0, x0[m - 1] = a, x0[m - 1] ∈ x0

Rule argument

Additional information

Used simplifier rules: e-01: ⊦ a ' + x ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-07: ⊦ (a ' + x).rest = x; from specification list