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Proof step 10 from proof sort-max-last (previous step)

a0 = a, sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ⊦ ins≤(a0, sort(x1 + x0) + a ') = ins≤(a0, sort(x1 + x0)) + a ', a < max((a0 ' + x1) + x0), a < max(x1 + x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ⊦ ins≤(a, sort(x1 + x0) + a ') = (sort(x1 + x0) + a ') + a ', a < max((a ' + x1) + x0), a < max(x1 + x0)

Rule argument

Additional information

Used simplifier rules: max-ins-max-last-sort: ⊦ ¬ a < max(x0) → ins≤(a, sort(x0)) = sort(x0) + a ';%a: ⊦ (x + y) + z = x + y + z; from specification list