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Proof step 8 from proof range-copy-lower (previous step)

m1 = n4 + n1, n1 ≤ m1, 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, m1) ↔ range=(ar2, n2, ar, n + n3, n1) ∧ range=(ar2, n1 + n2, ar0, n0 + n1 + n3, n4)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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)

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 ≤ m + n; (s)