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Proof step 22 from proof range-extend (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
n2 < m1, range=(copy(ar, n, ar0, n0 + m0, m1), n0, ar1, n1, m0), (n0 + m0) + m1 ≤ # ar0, (n1 + m0) + m1 ≤ # ar1, n + m1 ≤ # ar, n0 + m0 + m1 ≤ # ar0, ∀ n2. n2 < m1 → copy(ar, n, ar0, n0 + m0, m1)[(n0 + m0) + n2] = ar1[(n1 + m0) + n2] ⊦ ar[n + n2] = ar1[(n1 + m0) + n2]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # copy(ar, m, ar0, m0, n) = # ar0; (s)