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Proof step 7 from proof max-ins-max (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ordered≤(a ' + b ' + x) ↔ ¬ b < a ∧ ordered≤(b + x)
Proof step 9:
∀ a. max(ins≤(a, x0)) = a ∨ a < max(x0) ⊦ max(ins≤(a, a0 ' + x0)) = a, a < max(a0 ' + x0), ¬ a0 < a ∧ ordered≤(a0 + x0)

Rule argument

spec: olist inst: name: le-r seq: ⊦ ordered≤(a ' + b ' + x) ↔ ¬ b < a ∧ ordered≤(b + x) subst: [x, b, a] → [x0, a0, a] flags: rewrite

Additional information

Used terms: x0, a0, a