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Proof step 12 from proof ordered-append (previous step)

ordered≤(a ' + x1), ordered≤(x1 + a0 ' + y), ∀ x. ordered≤(x) ∧ (x ≠ [] → ¬ x.head < x1.last) → ordered≤(x1 + x) ⊦ x1 = [], a0 < x1.last, ordered≤(a ' + x1 + a0 ' + y)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.tail.head < y.head ∧ ordered≤(y.tail)
Proof step 14:
ordered≤(x1 + a0 ' + y), ordered≤(a ' + x1), ∀ x. ordered≤(x) ∧ (x ≠ [] → ¬ x.head < x1.last) → ordered≤(x1 + x) ⊦ x1 = [], a0 < x1.last, #(a ' + x1 + a0 ' + y) ≤ 1, ¬ (a ' + x1 + a0 ' + y).tail.head < (a ' + x1 + a0 ' + y).head ∧ ordered≤((a ' + x1 + a0 ' + y).tail)

Rule argument

spec: <toplevel> name: k-le-r seq: ⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.tail.head < y.head ∧ ordered≤(y.tail) subst: [y] → [a ' + x1 + a0 ' + y] flags: <all paths>

Additional information

Used terms: a ' + x1 + a0 ' + y