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Proof step 5 from proof at-save-out-upper (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ save(zbrar, m, nused + 1) = save(zbrar, m + 1, nused)[m, save(zbrar[m])]
Proof step 7:
(m + nused0) + 1 < BRANCH_SIZE, n < BRANCH_SIZE, m + nused0 < n, m + nused0 + 1 < BRANCH_SIZE, m + nused0 < BRANCH_SIZE, ∀ m, n, zbrar. m + nused0 < BRANCH_SIZE ∧ n < BRANCH_SIZE ∧ m + nused0 ≤ n → save(zbrar, m, nused0)[n] = mkbrarray(BRANCH_SIZE)[n] ⊦ save(zbrar, m + 1, nused0)[m, save(zbrar[m])][n] = mkbrarray(BRANCH_SIZE)[n]

Rule argument

spec: <toplevel> name: save-branches-rec seq: ⊦ save(zbrar, m, nused + 1) = save(zbrar, m + 1, nused)[m, save(zbrar[m])] subst: [nused, m, zbrar] → [nused0, m, zbrar] flags: <all paths>

Additional information

Used terms: nused0, m, zbrar