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Proof step 19 from proof max-ins-last (previous step)

a0 < a, max(x0) < a, ∀ a. max(x0) < a → ins≤(a, x0).last = a ⊦ (a0 ' + ins≤(a, x0)).last = a, x0 = [], max(x0) < a0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ x ≠ [] → (a ' + x).last = x.last
Proof step 21:
max(x0) < a, a0 < a, ∀ a. max(x0) < a → ins≤(a, x0).last = a ⊦ ins≤(a, x0).last = a, ins≤(a, x0) = [], x0 = [], max(x0) < a0

Rule argument

spec: list-last name: l-02 seq: ⊦ x ≠ [] → (a ' + x).last = x.last subst: [x, a] → [ins≤(a, x0), a0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ins≤(a, x) ≠ []; (s) Used terms: ins≤(a, x0), a0