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Proof step 32 from proof range-copy-inner (previous step)

n4 < n0, n1 + n0 + n3 + m0 ≤ # ar0, (n3 + n1) + m0 ≤ # ar0, n + m0 ≤ # ar, n2 + n0 + n3 + m0 ≤ # ar2, n4 + n3 + m0 < n0 + n3 + m0 → ar2[n2 + n4 + n3 + m0] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4 + n3 + m0], ∀ n4. n4 < n0 + n3 + m0 → ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4] ⊦ ar2[(n3 + n2 + m0) + n4] = ar0[((n3 + n1) + m0) + n4]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
ar2[n2 + n4 + n3 + m0] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4 + n3 + m0], n4 < n0, n2 + n0 + n3 + m0 ≤ # ar2, n + m0 ≤ # ar, (n3 + n1) + m0 ≤ # ar0, n1 + n0 + n3 + m0 ≤ # ar0, ∀ n4. n4 < n0 + n3 + m0 → ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4] ⊦ copy(ar, n, ar0, n3 + n1, m0)[n1 + n4 + n3 + m0] = ar0[((n3 + n1) + m0) + n4]

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)