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Proof step 4 from proof max-ins (previous step)

∀ a. max(ins≤(a, x0)) = max(x0) ∨ x0 = [] ∨ max(x0) < a ⊦ max(ins≤(a, a0 ' + x0)) = max(a0 ' + x0), max(a0 ' + x0) < a

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
x0 = [], ∀ a. max(ins≤(a, x0)) = max(x0) ∨ x0 = [] ∨ max(x0) < a ⊦ max(ins≤(a, a0 ' + x0)) = max(a0 ' + x0), max(a0 ' + x0) < a
Proof step 8:
∀ a. max(ins≤(a, x0)) = max(x0) ∨ x0 = [] ∨ max(x0) < a ⊦ x0 = [], max(ins≤(a, a0 ' + x0)) = max(a0 ' + x0), max(a0 ' + x0) < a

Rule argument

fma: x0 = []

Additional information

Used formulas: x0 = []