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Proof step 24 from proof sort-max-last (previous step)

sort(x1 + a ' + x0) = sort(x1 + x0) + a ', (max(x1 + x0) < a ⊃ a;max(x1 + x0)) < max(sort(x1 + x0) + 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)), max(x1 + x0) < a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
sort(x1 + max(x1 + x0) ' + x0) = sort(x1 + x0) + max(x1 + x0) ', max(x1 + x0) < max(sort(x1 + x0) + max(x1 + x0) '), ordered≤(sort(x1 + x0) + max(x1 + x0) ') ⊦ x1 + x0 = [], ins≤(max(x1 + x0), sort(x1 + x0) + max(x1 + x0) ') = (sort(x1 + x0) + max(x1 + x0) ') + max(x1 + x0) '

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)% ⊦ a ∈ sort(x) ↔ a ∈ x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list% ⊦ ¬ a < a; (s)%nen: ⊦ ¬ b < a ∧ a = c → ¬ b < c; (forward) from specification oelem%lel: ⊦ a < b ∧ a = c → c < b; (forward) from specification oelem% ⊦ ¬ b < a → (a < b ↔ a ≠ b); (ss)