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Proof step 1 from proof ins-rec (conclusion)

⊦ x ≠ [] ∧ x.first < a → ins≤(a, x) = x.first + ins≤(a, x.rest)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
x.first < a ⊦ x = [], ins≤(a, x) = x.first ' + ins≤(a, x.rest)

Rule argument

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x; from specification list