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Proof step 9 from proof max-ins-last (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 10:
max(x0) < a0, a0 < a, max(x0) < a, ∀ a. max(x0) < a → ins≤(a, x0).last = a ⊦ ins≤(a, x0) = [], x0 = [], (a0 ' + ins≤(a, x0)).last = a

Rule argument

fma: ins≤(a, x0) = []

Additional information

Used simplifier rules: empty: ⊦ ins≤(a, x) ≠ []; from specification olist Used formulas: ins≤(a, x0) = []