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Proof step 8 from proof sort-max-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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)

Rule argument

Additional information

Used simplifier rules: in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%in: ⊦ a ∈ sort(x) ↔ a ∈ x; from specification olist-sort%a: ⊦ (x + y) + z = x + y + z; from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list