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Proof step 2 from proof sort-max-last (previous step)

∀ a, x0. ¬ a < max(x1 + x0) → sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ⊦ ¬ a < max((a0 + x1) + x0) → sort((a0 + x1) + a ' + x0) = sort((a0 + x1) + x0) + a '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ a, x0. ¬ a < max(x1 + x0) → sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ⊦ ins≤(a0, sort(x1 + a ' + x0)) = ins≤(a0, sort(x1 + x0)) + a ', a < max((a0 ' + x1) + x0)

Rule argument

Additional information

Used simplifier rules: rec: ⊦ sort(a ' + x) = ins≤(a, sort(x)); from specification olist-sort%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list