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Proof step 8 from proof scan-lt (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
zbrar[m].key < key, m + n0 + 1 < scan(key, zbrar, m + 1, len0), ∀ m, n, key, zbrar. m + n < scan(key, zbrar, m, len0) → zbrar[m + n].key < key ⊦ zbrar[m + n0 + 1].key < key

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)