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Proof step 17 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ordered≤(a ' + x) → ins≤(a, x) = a ' + x
Proof step 19:
¬ ordered≤(a ' + x0), 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)

Rule argument

spec: olist inst: name: cons-03 seq: ⊦ ordered≤(a ' + x) → ins≤(a, x) = a ' + x subst: [x, a] → [x0, a] flags: rewrite

Additional information

Used simplifier rules: max-ge-first: ⊦ ¬ ¬ max(a ' + x) < a ↔ false;%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x0, a