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Proof step 2 from proof rangeeq-write-left-below (previous step)

n < m0 ⊦ range=(ar0[n, a], m0, ar1, m1, m) ↔ range=(ar0, m0, ar1, m1, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 4:
n < m0 ⊦ m0 + m ≤ # ar0[n, a] ∧ m1 + m ≤ # ar1 ∧ (∀ n2. n2 < m → ar0[n, a][m0 + n2] = ar1[m1 + n2]) ↔ range=(ar0, m0, ar1, m1, m)

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, m1, ar1, m0, ar0[n, a]] flags: <all paths>

Additional information

Used terms: m, m1, ar1, m0, ar0[n, a]