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Proof step 7 from proof at-last (previous step)

∀ m. # x0 = m + 1 → x0[m] = x0.last ∨ x0 = [] ⊦ x0 = [], (a ' + x0)[# x0] = (a ' + x0).last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ m. # x0 = m + 1 → x0[m] = x0.last ⊦ x0 = [], (a ' + x0)[# x0] = x0.last

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%l-02: ⊦ x ≠ [] → (a ' + x).last = x.last; from specification list-last