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

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

User applied rule apply lemma

And obtained the following new goals

Proof step 4:
⊦ sorted(zbrar, m, nused) ∧ n < len ∧ len ≤ nused ∧ m + nused ≤ # zbrar → scan(zbrar[m + n].key, zbrar, m, len) = m + n

Rule argument

spec: <toplevel> name: scan-given seq: ⊦ sorted(zbrar, m, nused) ∧ n < len ∧ len ≤ nused ∧ m + nused ≤ # zbrar → scan(zbrar[m + n].key, zbrar, m, len) = m + n subst: [zbrar, m, nused, n, len] → [zbrar, 0, nused, n, len]

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 Used terms: zbrar, 0, nused, n, len