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

x ≠ [], ordered≤(a0 ' + x), ∀ a1. ins≤(a1, x) = x + a1 ' ∨ a1 < max(x) ⊦ a ' + a0 ' + x = (a0 ' + x) + a ', a < (max(x) < a0 ⊃ a0;max(x)), a0 < a, a0 < (max(x) < a0 ⊃ a0;max(x))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
ordered≤(a0 ' + x), ∀ a1. ins≤(a1, x) = x + a1 ' ∨ a1 < max(x) ⊦ a ' + a0 ' + x = (a0 ' + x) + a ', x = [], a < (max(x) < a0 ⊃ a0;max(x)), a0 < a, a0 < (max(x) < a0 ⊃ a0;max(x))

Rule argument

Additional information

Used simplifier rules: nnn: ⊦ ¬ c < b ∧ ¬ a < c → ¬ a < b; (forward) from specification oelem