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Proof step 12 from proof range-extend (previous step)

range=(copy(ar, n, ar0, n0 + m0, m1), n0 + m0, ar1, n1 + m0, m1), n0 + m0 ≤ # ar0, n1 + m0 ≤ # ar1, n + m1 ≤ # ar, n0 + m0 + m1 ≤ # ar0, ∀ n2. n2 < m0 → copy(ar, n, ar0, n0 + m0, m1)[n0 + n2] = ar1[n1 + n2] ⊦ n0 + m0 ≤ # ar0 ∧ n1 + m0 ≤ # ar1 ∧ (∀ n. n < m0 → ar0[n0 + n] = ar1[n1 + n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
n2 < m0, range=(copy(ar, n, ar0, n0 + m0, m1), n0 + m0, ar1, n1 + m0, m1), n0 + m0 ≤ # ar0, n1 + m0 ≤ # ar1, n + m1 ≤ # ar, n0 + m0 + m1 ≤ # ar0, ∀ n2. n2 < m0 → copy(ar, n, ar0, n0 + m0, m1)[n0 + n2] = ar1[n1 + n2] ⊦ ar0[n0 + n2] = ar1[n1 + n2]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic