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Proof step 11 from proof del1-01 (previous step)

ordered≤(x0), ∀ a1. ordered≤(x0 -1l a1) ⊦ a = a0, x0 = [], x0.head < a0, ordered≤(a0 ' + (x0 -1l a))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
x0 = a2 + y, ordered≤(x0), ∀ a1. ordered≤(x0 -1l a1) ⊦ a = a0, x0 = [], a2 < a0, ordered≤(a0 ' + (x0 -1l a))

Rule argument

spec: list-data name: elim-list-c seq: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y subst: [x, a, y] → [x0, a2, y]

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: x0, a2, y