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Proof step 16 from proof range-copy-lower (previous step)

n2 + n4 + n1 ≤ # ar2, n0 ≤ # ar0, n3 + n0 ≤ # ar0, n0 + n1 + n3 ≤ # ar0, n + n1 + n3 ≤ # ar, (n3 + n0) + n4 + n1 ≤ # ar0, ∀ n5. n5 < n4 + n1 → ar2[n2 + n5] = copy(ar, n, ar0, n0, n1 + n3)[(n3 + n0) + n5] ⊦ n2 + n1 ≤ # ar2 ∧ (n + n3) + n1 ≤ # ar ∧ (∀ n4. n4 < n1 → ar2[n2 + n4] = ar[(n + n3) + n4])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
n5 < n1, n2 + n1 ≤ # ar2, (n3 + n0) + n4 + n1 ≤ # ar0, n + n1 + n3 ≤ # ar, n0 + n1 + n3 ≤ # ar0, n3 + n0 ≤ # ar0, n0 ≤ # ar0, n2 + n4 + n1 ≤ # ar2, ∀ n5. n5 < n4 + n1 → ar2[n2 + n5] = copy(ar, n, ar0, n0, n1 + n3)[(n3 + n0) + n5] ⊦ ar2[n2 + n5] = ar[(n + n3) + n5]

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ m + n < m; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic