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Proof step 11 from proof ordered-postfix (previous step)

ordered≤(x1), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ x1 = [], x1.head < a, ordered≤(x)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
x1 = a0 + y, ordered≤(x1), x ⊒ a ' + x1, ∀ x0. x0 ⊒ x1 → ordered≤(x0) ⊦ x1 = [], a0 < a, ordered≤(x)

Rule argument

spec: list-data name: elim-list-c seq: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y subst: [x, a, y] → [x1, a0, y]

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: x1, a0, y