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Proof step 3 from proof range-eq-trans (previous step)

range=(ar1, n1, ar2, n2, m), range=(ar0, n0, ar1, n1, m) ⊦ range=(ar0, n0, ar2, n2, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 5:
range=(ar0, n0, ar1, n1, m), range=(ar1, n1, ar2, n2, m) ⊦ n0 + m ≤ # ar0 ∧ n2 + m ≤ # ar2 ∧ (∀ n. n < m → ar0[n0 + n] = ar2[n2 + n])

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, n2, ar2, n0, ar0] flags: <all paths>

Additional information

Used terms: m, n2, ar2, n0, ar0