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Proof step 41 from proof range-copy-inner (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
n4 < n0 + n3 + m0, range=(ar2, n2, ar0, n1, n3), range=(ar2, n3 + n2, ar, n, m0), n + m0 ≤ # ar, (n3 + n1) + m0 ≤ # ar0, (n3 + n2 + m0) + n0 ≤ # ar2, ((n3 + n1) + m0) + n0 ≤ # ar0, ∀ n. n < n0 → ar2[(n3 + n2 + m0) + n] = ar0[((n3 + n1) + m0) + n] ⊦ ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[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