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Proof step 32 from proof range-copy-lower (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 34:
range=(ar2, n1 + n2, ar0, n0 + n1 + n3, n4), n0 ≤ # ar0, n3 + n0 ≤ # ar0, n0 + n1 + n3 ≤ # ar0, n + n1 + n3 ≤ # ar, n2 + n1 ≤ # ar2, (n + n3) + n1 ≤ # ar, ∀ n4. n4 < n1 → ar2[n2 + n4] = ar[(n + n3) + n4] ⊦ n2 + n4 + n1 ≤ # ar2 ∧ (n3 + n0) + n4 + n1 ≤ # ar0 ∧ (n5 < n4 + n1 → ar2[n2 + n5] = copy(ar, n, ar0, n0, n1 + n3)[(n3 + n0) + n5])

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