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Proof step 4 from proof get-butlast (previous step)

n ≤ # x0, ∀ n, a. n < # x0 → (x0 + a ')[n] = x0[n] ∨ x0 = [] ⊦ ((a0 ' + x0) + a ')[n] = (a0 ' + x0)[n]

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
n ≤ # x0, ∀ n, a. n < # x0 → (x0 + a ')[n] = x0[n] ∨ x0 = [] ⊦ x0 = [], ((a0 ' + x0) + a ')[n] = (a0 ' + x0)[n]

Rule argument

fma: x0 = []

Additional information

Used simplifier rules: get-zero-01: ⊦ (a ' + x)[0] = a;%one-03: ⊦ a '[0] = a;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%app: ⊦ x + [] = x; from specification list%size-01: ⊦ # [] = 0; from specification list-data%lez-01: ⊦ m ≤ 0 ↔ m = 0; from specification nat%zero-01: ⊦ ¬ m < 0; from specification nat-basic1 Used formulas: x0 = []