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Proof step 18 from proof range-copy-inner (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4], n4 < n0 + n3 + m0, n4 < n3, n2 + n3 ≤ # ar2, n1 + n3 ≤ # ar0, n1 + n0 + n3 + m0 ≤ # ar0, (n3 + n1) + m0 ≤ # ar0, n + m0 ≤ # ar, n2 + n0 + n3 + m0 ≤ # ar2, ∀ n4. n4 < n0 + n3 + m0 → ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4] ⊦ ar2[n2 + n4] = ar0[n1 + n4]

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% ⊦ ¬ m + n < m; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)