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Proof step 7 from proof max-ins-last (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
max(x0) < a0, (max(x0) < a0 ⊃ a0;max(x0)) < a, ∀ a. max(x0) < a → ins≤(a, x0).last = a ⊦ ins≤(a, a0 ' + x0).last = a, x0 = []
Proof step 15:
(max(x0) < a0 ⊃ a0;max(x0)) < a, ∀ a. max(x0) < a → ins≤(a, x0).last = a ⊦ max(x0) < a0, ins≤(a, a0 ' + x0).last = a, x0 = []

Rule argument

fma: max(x0) < a0

Additional information

Used formulas: max(x0) < a0