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Proof step 3 from proof at-save (previous step)

n < nused0 +1, m + nused0 +1 ≤ BRANCH_SIZE, ∀ n, m, zbrar. n < nused0 ∧ m + nused0 ≤ BRANCH_SIZE → save(zbrar, m, nused0)[m + n] = save(zbrar[m + n]) ⊦ save(zbrar, m, nused0 +1)[m + n] = save(zbrar[m + n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
m + nused0 < BRANCH_SIZE, n ≤ nused0, ∀ n, m, zbrar. n < nused0 ∧ m + nused0 ≤ BRANCH_SIZE → save(zbrar, m, nused0)[m + n] = save(zbrar[m + n]) ⊦ save(zbrar, m, nused0 + 1)[m + n] = save(zbrar[m + n])

Rule argument

Additional information

Used simplifier rules: ⊦ BRANCH_SIZE ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)