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Proof step 27 from proof max-ordered (previous step)

max(x0) < max(x1), a < max(x1), max(x0) < a, x1 ⊑ x0, ∀ m, n. m ≤ n ∧ n < # x0 → ¬ x0[n] < x0[m] ⊦ max(x1) = a, x0 = [], x1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ x ⊑ y ↔ (∃ z. x + z = y)

Rule argument

spec: list-last name: prefix seq: ⊦ x ⊑ y ↔ (∃ z. x + z = y) subst: [y, x] → [x0, x1] flags: <all paths>

Additional information

Used simplifier rules: max-ge: ⊦ x ≠ [] → (max(x + x0) < max(x) ↔ false);%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x0, x1