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

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

User applied rule structural induction

And obtained the following new goals

Proof step 4:
scan(key, zbrar, m, len0 +1) < m + len0 +1, zbrar[scan(key, zbrar, m, len0 +1)].key < key, ∀ zbrar, key, m. ¬(zbrar[scan(key, zbrar, m, len0)].key < key ∧ scan(key, zbrar, m, len0) < m + len0) ⊦

Rule argument

indvar: len

Additional information

Used simplifier rules: scan-base: ⊦ scan(key, zbrar, m, 0) = m;%nat freely generated by 0, +1;;% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ n < n; (s)