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Proof step 12 from proof cut (previous step)

⊦ ar = [], # ar = # copy(subarray(ar, 1, # ar - 1), 0, mkarray(# subarray(ar, 1, # ar - 1) + 1), 1, # subarray(ar, 1, # ar - 1))[0, ar[0]] ∧ (n < # ar → ar[n] = copy(subarray(ar, 1, # ar - 1), 0, mkarray(# subarray(ar, 1, # ar - 1) + 1), 1, # subarray(ar, 1, # ar - 1))[0, ar[0]][n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
⊦ ar = [], # ar = (# ar - 1) + 1 ∧ (n < # ar → ar[n] = copy(ar, 1, mkarray((# ar - 1) + 1), 1, # ar - 1)[0, ar[0]][n])

Rule argument

Additional information

Used simplifier rules: copy-subarray1-elim: n0 + n1 ≤ # ar0, m + m1 ≤ n1 ⊦ copy(subarray(ar0, n0, n1), m, ar1, m0, m1) = copy(ar0, n0 + m, ar1, m0, m1); from specification array-copy%sub-ls: ⊦ ¬ n + (m - n) < m; from specification nat%ls-03: n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-base: ⊦ n + 0 = n; from specification nat-basic2%ler: ⊦ m ≤ m; from specification nat%Size-mkarray: ⊦ # mkarray(n) = n; from specification array%size-copy: ⊦ # copy(ar, m, ar0, m0, n) = # ar0; from specification array-copy%Size-put: ⊦ # ar[n, a] = # ar; from specification array%size-subarray: ⊦ # subarray(ar, m, n) = n; from specification array-copy