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

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

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: len

Additional information

Used simplifier rules: scan-base: ⊦ scan(key, zbrar, m, 0) = m;%nat freely generated by 0, +1;;% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic