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Proof step 4 from proof copy-subarray1-elim (previous step)

n0 + n1 ≤ # ar0, m + m1 ≤ n1 ⊦ # copy(copy(ar0, n0, mkarray(n1), 0, n1), m, ar1, m0, m1) = # copy(ar0, n0 + m, ar1, m0, m1) ∧ (∀ n. n < # copy(copy(ar0, n0, mkarray(n1), 0, n1), m, ar1, m0, m1) → copy(copy(ar0, n0, mkarray(n1), 0, n1), m, ar1, m0, m1)[n] = copy(ar0, n0 + m, ar1, m0, m1)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n0 + n1 ≤ # ar0, m + m1 ≤ n1, n < # ar1 ⊦ (n < m0 ∨ m0 + m1 ≤ n ⊃ ar1[n];copy(ar0, n0, mkarray(n1), 0, n1)[n + m - m0]) = (n < m0 ∨ m0 + m1 ≤ n ⊃ ar1[n];ar0[n + n0 + m - m0]), # ar1 = 0

Rule argument

Additional information

Used simplifier rules: size-copy: ⊦ # copy(ar, m, ar0, m0, n) = # ar0;%at-copy: ⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0]);%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1