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Proof step 12 from proof ole-last (previous step)

ordered≤(x0 + a '), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a, (x0 + a ').head < a0, ordered≤((a0 ' + x0) + a ' + b ')

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
x0 + a ' = a1 + y, ordered≤(x0 + a '), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ x0 + a ' = [], a1 < a0, b < a, ordered≤((a0 ' + x0) + a ' + b ')

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 + a ', a1, y]

Additional information

Used simplifier rules: ⊦ x + y = [] ↔ x = [] ∧ y = []; (as)% ⊦ a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: x0 + a ', a1, y