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Proof step 2 from proof at-save-0 (previous step)

n < nused, n < BRANCH_SIZE, nused ≤ BRANCH_SIZE ⊦ save(zbrar, 0, nused)[n] = save(zbrar[n])

User applied rule apply lemma

And obtained the following new goals

Proof step 3:
n < nused, m + nused ≤ BRANCH_SIZE ⊦ save(zbrar, m, nused)[m + n] = save(zbrar[m + n])

Rule argument

spec: <toplevel> name: at-save seq: n < nused, m + nused ≤ BRANCH_SIZE ⊦ save(zbrar, m, nused)[m + n] = save(zbrar[m + n]) subst: [n, nused, m, zbrar] → [n, nused, 0, zbrar]

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s) Used terms: n, nused, 0, zbrar