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Proof step 5 from proof scan-lt (previous step)

m + n < (¬ zbrar[m].key < key ⊃ m;scan(key, zbrar, m + 1, len0)), ∀ m, n, key, zbrar. m + n < scan(key, zbrar, m, len0) → zbrar[m + n].key < key ⊦ zbrar[m + n].key < key

User applied rule case distinction

And obtained the following new goals

Proof step 6:
m + n < scan(key, zbrar, m + 1, len0), zbrar[m].key < key, ∀ m, n, key, zbrar. m + n < scan(key, zbrar, m, len0) → zbrar[m + n].key < key ⊦ zbrar[m + n].key < key

Rule argument

pos: left 1

Additional information

Used simplifier rules: ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic