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Proof step 8 from proof scan-strong (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ n < scan(key, zbrar, 0, len) ∧ n ≠ len → zbrar[n].key < key

Rule argument

spec: <toplevel> name: scan-lt-0 seq: ⊦ n < scan(key, zbrar, 0, len) ∧ n ≠ len → zbrar[n].key < key subst: [len, key, n, zbrar] → [nused, key, n, zbrar] flags: <all paths>

Additional information

Used simplifier rules: lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s) Used terms: nused, key, n, zbrar