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

n < len, n < nused, sorted(zbrar, m, nused), m + nused ≤ # zbrar, len ≤ nused ⊦ scan(zbrar[m + n].key, zbrar, m, len) = m + n

User applied rule structural induction

And closed the goal!

Rule argument

term: zbrar[m + n]

Additional information

Used simplifier rules: scan-branch: ⊦ zbrar[m + n] = mkzbranch(key, adr, r) ∧ sorted(zbrar, m, nused) ∧ n < len ∧ len ≤ nused ∧ m + nused ≤ # zbrar → scan(key, zbrar, m, len) = m + n;%scan-entry: ⊦ zbrar[m + n] = mkzentry(key, adr) ∧ sorted(zbrar, m, nused) ∧ n < len ∧ len ≤ nused ∧ m + nused ≤ # zbrar → scan(key, zbrar, m, len) = m + n;%zbranch freely generated by mkzbranch, mkzentry;;% ⊦ mkzentry(key, adr).key = key; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ mkzbranch(key, adr, r).key = key; (s)