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Proof step 20 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 21:
⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.rest.first < y.first ∧ ordered≤(y.rest)
Proof step 22:
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), #(a ' + x0) ≤ 1 ∨ ¬ (a ' + x0).rest.first < (a ' + x0).first ∧ ordered≤((a ' + x0).rest)

Rule argument

spec: olist inst: name: k-le-r seq: ⊦ ordered≤(y) ↔ # y ≤ 1 ∨ ¬ y.rest.first < y.first ∧ ordered≤(y.rest) subst: [y] → [a ' + x0] flags: rewrite

Additional information

Used terms: a ' + x0