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Proof step 9 from proof scan-lt (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: m + 1, n0, key, zbrar abort: F discard: F computed: F

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m + 1, n0, key, zbrar