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Proof step 11 from proof ole-last (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
x0 + a ' = a1 + y ∧ x0 + a ' ≠ [], ordered≤(x0 + a '), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ b < a, ordered≤((a0 ' + x0) + a ' + b '), a1 < a0

Rule argument

spec: list-data inst: name: elim-list-c seq: x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y subst: [x, a, y] → [x0 + a ', a1, y] flags:

Additional information

Used simplifier rules: app-02-ant: ⊦ ¬ x + y ≠ [] ↔ x = [] ∧ y = []; from specification list%e: ⊦ a ' ≠ []; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y; (elim) Used terms: x0 + a ', a1, y