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Proof step 4 from proof scan-max (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m + len0 + 1 < (¬ zbrar[m].key < key ⊃ m;scan(key, zbrar, m + 1, len0)), ∀ m, key, zbrar. ¬ m + len0 < scan(key, zbrar, m, len0) ⊦

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));% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ key0 ≤ key1 ↔ ¬ key1 < key0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)