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Proof step 6 from proof at-last (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
∀ m. # x0 = m + 1 → x0[m] = x0.last ∨ x0 = [] ⊦ x0 = [], (a ' + x0)[# x0] = (a ' + x0).last

Rule argument

fma: x0 = []

Additional information

Used simplifier rules: one-03: ⊦ a '[0] = a;%app: ⊦ x + [] = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%size-01: ⊦ # [] = 0; from specification list-data%l: ⊦ a '.last = a; from specification list-last Used formulas: x0 = []