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

scan(key, zbrar, m, len0 +1) < m, ∀ key, zbrar, m. ¬ scan(key, zbrar, m, len0) < m ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: scan-rec: ⊦ scan(key, zbrar, m, n + 1) = (key ≤ zbrar[m].key ⊃ m;scan(key, zbrar, m + 1, n));%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ key0 ≤ key1 ↔ ¬ key1 < key0; (s)% ⊦ m +1 = m + 1; (s)