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Proof step 11 from proof range-copy-outer (previous step)

(n3 + n0) + m1 ≤ # ar0, n + m0 ≤ # ar, n0 + m0 ≤ # ar0, n3 + m1 ≤ m0, n2 + m1 ≤ # ar2, ∀ n4. n4 < m1 → ar2[n2 + n4] = copy(ar, n, ar0, n0, m0)[(n3 + n0) + n4] ⊦ n2 + m1 ≤ # ar2 ∧ (n + n3) + m1 ≤ # ar ∧ (∀ n4. n4 < m1 → ar2[n2 + n4] = ar[(n + n3) + n4])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n1 < m1, (n + n3) + m1 ≤ # ar, n2 + m1 ≤ # ar2, n3 + m1 ≤ m0, n0 + m0 ≤ # ar0, n + m0 ≤ # ar, (n3 + n0) + m1 ≤ # ar0, ∀ n4. n4 < m1 → ar2[n2 + n4] = copy(ar, n, ar0, n0, m0)[(n3 + n0) + n4] ⊦ ar2[n2 + n1] = ar[(n + n3) + n1]

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 → (n < m ↔ false); (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)