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

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

User applied rule case distinction

And obtained the following new goals

Proof step 12:
n1 + n0 + n3 ≤ # ar0, n3 + n1 ≤ # ar0, n1 ≤ # ar0, (n3 + n1) + m0 ≤ # ar0, n + m0 ≤ # ar, n0 ≤ m0, n2 + n0 + n3 ≤ # ar2, ∀ n4. n4 < n0 + n3 → ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4] ⊦ range=(ar2, n2, ar0, n1, n3)
Proof step 19:
n1 + n0 + n3 ≤ # ar0, n3 + n1 ≤ # ar0, n1 ≤ # ar0, (n3 + n1) + m0 ≤ # ar0, n + m0 ≤ # ar, n0 ≤ m0, n2 + n0 + n3 ≤ # ar2, ∀ n4. n4 < n0 + n3 → ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4] ⊦ range=(ar2, n3 + n2, ar, n, n0)

Rule argument

pos: right 1

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

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information