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Proof step 7 from proof range-copy-upper (previous step)

n3 + n1 ≤ # ar0, n1 ≤ # ar0, n1 + n0 + n3 ≤ # ar0, (n3 + n1) + m0 ≤ # ar0, n + m0 ≤ # ar, n0 ≤ m0 ⊦ range=(ar2, n2, copy(ar, n, ar0, n3 + n1, m0), n1, n0 + n3) ↔ 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 8:
range=(ar2, n2, copy(ar, n, ar0, n3 + n1, m0), n1, n0 + n3), n0 ≤ m0, n + m0 ≤ # ar, (n3 + n1) + m0 ≤ # ar0, n1 + n0 + n3 ≤ # ar0, n1 ≤ # ar0, n3 + n1 ≤ # ar0 ⊦ range=(ar2, n2, ar0, n1, n3) ∧ range=(ar2, n3 + n2, ar, n, n0)
Proof step 26:
range=(ar2, n2, ar0, n1, n3), range=(ar2, n3 + n2, ar, n, n0), n0 ≤ m0, n + m0 ≤ # ar, (n3 + n1) + m0 ≤ # ar0, n1 + n0 + n3 ≤ # ar0, n1 ≤ # ar0, n3 + n1 ≤ # ar0 ⊦ range=(ar2, n2, copy(ar, n, ar0, n3 + n1, m0), n1, n0 + n3)

Rule argument

pos: right 1

Proof step 7 from proof range-copy-upper (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information