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Proof step 10 from proof at-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ m. # x0 = m + 1 → x0[m] = x0.last ⊦ x0 = [], x0[# x0 - 1] = x0.last

Rule argument

Additional information

Used simplifier rules: e-01: ⊦ a ' + x ≠ []; from specification list%l: ⊦ # x = 0 ↔ x = []; from specification list-data%a: ⊦ (x + y) + z = x + y + z; from specification list%c-07: ⊦ (a ' + x).rest = x; from specification list