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Proof step 16 from proof del1-01 (previous step)

ordered≤(a2 ' + y), ∀ a1. ordered≤((a2 ' + y) -1l a1) ⊦ (a2 ' + y) -1l a = [], a = a0, a2 < a0, ¬ ((a2 ' + y) -1l a).head < a0 ∧ ordered≤((a2 ' + y) -1l a)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: list-data name: elim-list-c seq: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y subst: [x, a, y] → [(a2 ' + y) -1l a, a3, y0]

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: (a2 ' + y) -1l a, a3, y0