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Proof step 3 from proof scan-le-0 (previous step)

zbrar[scan(key, zbrar, 0, len)].key < key, scan(key, zbrar, 0, len) < len ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ scan(key, zbrar, m, len) < m + len → ¬ zbrar[scan(key, zbrar, m, len)].key < key

Rule argument

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

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: len, 0, key, zbrar