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Proof step 9 from proof range-copy-lower (previous step)

n + n1 + n3 ≤ # ar, n0 + n1 + n3 ≤ # ar0, n3 + n0 ≤ # ar0, n0 ≤ # ar0 ⊦ range=(ar2, n2, copy(ar, n, ar0, n0, n1 + n3), n3 + n0, n4 + n1) ↔ range=(ar2, n2, ar, n + n3, n1) ∧ range=(ar2, n1 + n2, ar0, n0 + n1 + n3, n4)

User applied rule case distinction

And obtained the following new goals

Proof step 10:
range=(ar2, n2, copy(ar, n, ar0, n0, n1 + n3), n3 + n0, n4 + n1), n0 ≤ # ar0, n3 + n0 ≤ # ar0, n0 + n1 + n3 ≤ # ar0, n + n1 + n3 ≤ # ar ⊦ range=(ar2, n2, ar, n + n3, n1) ∧ range=(ar2, n1 + n2, ar0, n0 + n1 + n3, n4)
Proof step 28:
range=(ar2, n2, ar, n + n3, n1), range=(ar2, n1 + n2, ar0, n0 + n1 + n3, n4), n0 ≤ # ar0, n3 + n0 ≤ # ar0, n0 + n1 + n3 ≤ # ar0, n + n1 + n3 ≤ # ar ⊦ range=(ar2, n2, copy(ar, n, ar0, n0, n1 + n3), n3 + n0, n4 + n1)

Rule argument

pos: right 1

Proof step 9 from proof range-copy-lower (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information