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Proof step 45 from proof range-copy-inner (previous step)

n4 < n0 + n3 + m0, range=(ar2, n2, ar0, n1, n3), n + m0 ≤ # ar, (n3 + n2) + m0 ≤ # ar2, (n3 + n1) + m0 ≤ # ar0, (n3 + n2 + m0) + n0 ≤ # ar2, ((n3 + n1) + m0) + n0 ≤ # ar0, ∀ n4. n4 < m0 → ar2[(n3 + n2) + n4] = ar[n + n4], ∀ n. n < n0 → ar2[(n3 + n2 + m0) + n] = ar0[((n3 + n1) + m0) + n] ⊦ ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[n1 + n4]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 47:
n4 < n0 + n3 + m0, ((n3 + n1) + m0) + n0 ≤ # ar0, (n3 + n2 + m0) + n0 ≤ # ar2, (n3 + n1) + m0 ≤ # ar0, (n3 + n2) + m0 ≤ # ar2, n + m0 ≤ # ar, n2 + n3 ≤ # ar2, n1 + n3 ≤ # ar0, ∀ n. n < n0 → ar2[(n3 + n2 + m0) + n] = ar0[((n3 + n1) + m0) + n], ∀ n4. n4 < m0 → ar2[(n3 + n2) + n4] = ar[n + n4], ∀ n. n < n3 → ar2[n2 + n] = ar0[n1 + n] ⊦ ar2[n2 + n4] = copy(ar, n, ar0, n3 + n1, m0)[n1 + 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] → [n3, n1, ar0, n2, ar2] flags: <all paths>

Additional information

Used terms: n3, n1, ar0, n2, ar2