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Proof step 26 from proof copy-shift-right (previous step)

n < # ar0 + # ar1 ⊦ ar[n + m - n0 + # ar0] = (n < # ar0 ⊃ ar0[n];copy(ar, m, ar1, n0, m1)[n - # ar0]), n < n0 + # ar0, (n0 + # ar0) + m1 ≤ n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
n0 < # ar1, n < # ar0 + # ar1, n < (n0 + # ar0) + m1, n0 + # ar0 ≤ n ⊦ ar[(n - n0 + # ar0) + m] = copy(ar, m, ar1, n0, m1)[n - # ar0], m1 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ m + n < m; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n ↔ ¬ n < m; (ss)