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

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

User applied rule structural induction

And obtained the following new goals

Proof step 3:
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])

Rule argument

indvar: nused

Additional information

Used simplifier rules: save-branches-base: ⊦ save(zbrar, m, 0) = mkbrarray(BRANCH_SIZE);%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% ⊦ ¬ m < 0; (s)