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Proof step 9 from proof range-eq-trans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 11:
n2 + m ≤ # ar2, n0 + m ≤ # ar0, n1 + m ≤ # ar1, ∀ n. n < m → ar1[n1 + n] = ar2[n2 + n], ∀ n. n < m → ar0[n0 + n] = ar1[n1 + n] ⊦ n0 + m ≤ # ar0 ∧ (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, n1, ar1, n0, ar0] flags: <all paths>

Additional information

Used terms: m, n1, ar1, n0, ar0