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

zbrar[m + n] = mkzentry(key, adr), n < nused, len0 < nused, sorted(zbrar, m, nused), m + nused ≤ # zbrar, n ≤ len0, ∀ zbrar, m, n, key, adr, nused. zbrar[m + n] = mkzentry(key, adr) ∧ n < len0 ∧ n < nused ∧ sorted(zbrar, m, nused) ∧ m + nused ≤ # zbrar ∧ len0 ≤ nused → scan(key, zbrar, m, len0) = m + n ⊦ (0 = n ⊃ m;scan(key, zbrar, m + 1, len0)) = m + n

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
zbrar[m + n] = mkzentry(key, adr), n = n0 +1, len0 < nused, n < nused, sorted(zbrar, m, nused), n ≤ len0, m + nused ≤ # zbrar, ∀ zbrar, m, n, key, adr, nused. zbrar[m + n] = mkzentry(key, adr) ∧ n < len0 ∧ n < nused ∧ sorted(zbrar, m, nused) ∧ m + nused ≤ # zbrar ∧ len0 ≤ nused → scan(key, zbrar, m, len0) = m + n ⊦ (0 = n ⊃ m;scan(key, zbrar, m + 1, len0)) = m + n

Rule argument

var: n

Additional information

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