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Proof step 24 from proof max-ordered (previous step)

max(x0) < a, ordered≤(x0), x1 ⊑ x0, a < max(x1), max(x0) < max(x1) ⊦ x0 = [], max(x1) = a, x1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ ordered≤(x) ↔ (∀ m, n. m ≤ n ∧ n < # x → ¬ x[n] < x[m])
Proof step 26:
max(x0) < a, ∀ m, n. m ≤ n ∧ n < # x0 → ¬ x0[n] < x0[m], x1 ⊑ x0, a < max(x1), max(x0) < max(x1) ⊦ x0 = [], max(x1) = a, x1 = []

Rule argument

spec: olist inst: name: orderedle-all seq: ⊦ ordered≤(x) ↔ (∀ m, n. m ≤ n ∧ n < # x → ¬ x[n] < x[m]) subst: [x] → [x0] flags: rewrite

Additional information

Used terms: x0