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Proof step 5 from proof scan-strong (previous step)

scan(key, zbrar, 0, nused) < # zbrar, scan(key, zbrar, 0, nused) + 1 < nused, n0 < nused, scan(key, zbrar, 0, nused) < n0, n0 < # zbrar, scan(key, zbrar, 0, nused) < nused, scan(key, zbrar, 0, nused) + 1 < # zbrar, sorted(zbrar, 0, nused), nused ≤ # zbrar ⊦ key < zbrar[n0].key

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: scan-le-0 seq: ⊦ scan(key, zbrar, 0, len) < len → ¬ zbrar[scan(key, zbrar, 0, len)].key < key subst: [key, zbrar, len] → [key, zbrar, nused]

Additional information

Used simplifier rules: nnn: ⊦ ¬ key1 < key0 ∧ ¬ key < key1 → ¬ key < key0; (forward) from specification oelem[key-order]%⊦ m0 < m ∧ m1 < m ∧ sorted(zbrar, 0, m) → (zbrar[m0].key < zbrar[m1].key ↔ m0 < m1); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: key, zbrar, nused