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Proof step 13 from proof ordered-prefix (previous step)

x1 ⊑ y, (∃ x0. ordered≤(x0) ∧ x1 ⊑ x0) → ordered≤(x1), y = [] ∨ ¬ y.head < a ∧ ordered≤(y) ⊦ ordered≤(a ' + x1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.tail.head < y.head ∧ ordered≤(y.tail)
Proof step 15:
x1 ⊑ y, (∃ x0. ordered≤(x0) ∧ x1 ⊑ x0) → ordered≤(x1), y = [] ∨ ¬ y.head < a ∧ ordered≤(y) ⊦ #(a ' + x1) ≤ 1, ¬ (a ' + x1).tail.head < (a ' + x1).head ∧ ordered≤((a ' + x1).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] flags: <all paths>

Additional information

Used terms: a ' + x1