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Proof step 5 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 6:
n ≤ # x0, ∀ n, a. n < # x0 → (x0 + a ')[n] = x0[n] ∨ x0 = [] ⊦ ((a0 ' + x0) + a ')[n] = (a0 ' + x0)[n], x0 = []

Rule argument

fma: x0 = []

Additional information

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