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Proof step 1 from proof ins-less-first (conclusion)

⊦ ordered≤(x) ∧ x ≠ [] ∧ ¬ a < x.head → ins≤(a, x) = x.head + ins≤(a, x.tail)

System applied rule normalize

And obtained the following new goals

Proof step 2:
ordered≤(x) ⊦ ins≤(a, x) = x.head + ins≤(a, x.tail), x = [], a < x.head

Rule argument

Additional information