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Proof step 7 from proof at-save-out-upper (previous step)

(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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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 + 1, nused0)[n] = mkbrarray(BRANCH_SIZE)[n]

Rule argument

Additional information

Used simplifier rules: ⊦ m + m0 < n → brar[m, br][n] = brar[n]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic