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Proof step 21 from proof max-ins-max (previous step)

max(ins≤(a, x0)) < a0, a0 < a, max(ins≤(a, x0)) < a, ∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ a0 = a, a < max(a0 ' + x0), ordered≤(a ' + x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.tail.head < y.head ∧ ordered≤(y.tail)
Proof step 23:
max(ins≤(a, x0)) < a, a0 < a, max(ins≤(a, x0)) < a0, ∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ a0 = a, a < max(a0 ' + x0), #(a ' + x0) ≤ 1, ¬ (a ' + x0).tail.head < (a ' + x0).head ∧ ordered≤((a ' + x0).tail)

Rule argument

spec: olist name: k-le-r seq: ⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.tail.head < y.head ∧ ordered≤(y.tail) subst: [y] → [a ' + x0] flags: <all paths>

Additional information

Used terms: a ' + x0