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Proof step 19 from proof sort-max-last (previous step)

sort(x1 + a ' + x0) = sort(x1 + x0) + a ', max(x1 + x0) < max(sort(x1 + x0) + a '), (max(x1 + x0) < a ⊃ a;max(x1 + x0)) < max(sort(x1 + x0) + a '), a < max(sort(x1 + x0) + a '), ordered≤(sort(x1 + x0) + a ') ⊦ x1 + x0 = [], ins≤(a, sort(x1 + x0) + a ') = (sort(x1 + x0) + a ') + a ', a < max(x1 + x0), a < (max(x1 + x0) < a ⊃ a;max(x1 + x0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
sort(x1 + a ' + x0) = sort(x1 + x0) + a ', a < max(sort(x1 + x0) + a '), max(x1 + x0) < max(sort(x1 + x0) + a '), (max(x1 + x0) < a ⊃ a;max(x1 + x0)) < max(sort(x1 + x0) + a '), ordered≤(sort(x1 + x0) + a ') ⊦ x1 + x0 = [], ins≤(a, sort(x1 + x0) + a ') = (sort(x1 + x0) + a ') + a ', a < (max(x1 + x0) < a ⊃ a;max(x1 + x0)), a < max(x1 + x0)

Rule argument

Additional information

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