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

⊦ scan(key, zbrar, m, n) = m, zbrar[m].key < key

User applied rule constructor cut

And closed the goal!

Rule argument

var: n

Additional information

Used simplifier rules: scan-base: ⊦ scan(key, zbrar, m, 0) = m;%scan-rec: ⊦ scan(key, zbrar, m, n + 1) = (key ≤ zbrar[m].key ⊃ m;scan(key, zbrar, m + 1, n));%nat freely generated by 0, +1;;% ⊦ m +1 = m + 1; (s)% ⊦ key0 ≤ key1 ↔ ¬ key1 < key0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic