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Proof step 18 from proof range-eq-resize (previous step)

n1 + m ≤ # ar1, n0 + m ≤ # ar0, n ≤ # ar1, m + n1 ≤ n, m + n1 ≤ # ar1, ∀ n. n < m → ar0[n0 + n] = ar1[n1 + n] ⊦ range=(ar0, n0, resize(ar1, n), n1, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 20:
m + n1 ≤ # ar1, m + n1 ≤ n, n ≤ # ar1, n0 + m ≤ # ar0, n1 + m ≤ # ar1, ∀ n. n < m → ar0[n0 + n] = ar1[n1 + n] ⊦ n0 + m ≤ # ar0 ∧ n1 + m ≤ # resize(ar1, n) ∧ (∀ n2. n2 < m → ar0[n0 + n2] = resize(ar1, n)[n1 + n2])

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] → [m, n1, resize(ar1, n), n0, ar0] flags: <all paths>

Additional information

Used terms: m, n1, resize(ar1, n), n0, ar0