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Proof step 7 from proof scan-lt (previous step)

m + n < scan(key, zbrar, m + 1, len0), zbrar[m].key < key, ∀ m, n, key, zbrar. m + n < scan(key, zbrar, m, len0) → zbrar[m + n].key < key ⊦ zbrar[m + n].key < key

User applied rule constructor cut

And obtained the following new goals

Proof step 8:
n = n0 +1, zbrar[m].key < key, m + n < scan(key, zbrar, m + 1, len0), ∀ m, n, key, zbrar. m + n < scan(key, zbrar, m, len0) → zbrar[m + n].key < key ⊦ zbrar[m + n].key < key

Rule argument

var: n

Additional information

Used simplifier rules: 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