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Proof step 14 from proof range-copy-lower (previous step)

(n3 + n0) + n4 + n1 ≤ # ar0, n + n1 + n3 ≤ # ar, n0 + n1 + n3 ≤ # ar0, n3 + n0 ≤ # ar0, n0 ≤ # ar0, n2 + n4 + n1 ≤ # ar2, ∀ n5. n5 < n4 + n1 → ar2[n2 + n5] = copy(ar, n, ar0, n0, n1 + n3)[(n3 + n0) + n5] ⊦ range=(ar2, n2, ar, n + n3, n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 16:
n2 + n4 + n1 ≤ # ar2, n0 ≤ # ar0, n3 + n0 ≤ # ar0, n0 + n1 + n3 ≤ # ar0, n + n1 + n3 ≤ # ar, (n3 + n0) + n4 + n1 ≤ # ar0, ∀ n5. n5 < n4 + n1 → ar2[n2 + n5] = copy(ar, n, ar0, n0, n1 + n3)[(n3 + n0) + n5] ⊦ n2 + n1 ≤ # ar2 ∧ (n + n3) + n1 ≤ # ar ∧ (∀ n4. n4 < n1 → ar2[n2 + n4] = ar[(n + n3) + n4])

Rule argument

spec: <toplevel> name: range-eq-ext seq: ⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n]) subst: [m, n1, ar1, n0, ar0] → [n1, n + n3, ar, n2, ar2] flags: <all paths>

Additional information

Used terms: n1, n + n3, ar, n2, ar2