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

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

User applied rule apply lemma

And obtained the following new goals

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

Rule argument

spec: <toplevel> name: scan-lt seq: ⊦ m + n < scan(key, zbrar, m, len) → zbrar[m + n].key < key subst: [m, n, key, zbrar, len] → [0, n, key, zbrar, 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: 0, n, key, zbrar, len