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Proof step 1 from proof range-eq-shift-right (conclusion)

⊦ range=(ar0 + ar1, # ar0 + m, ar, m0, m1) ↔ range=(ar1, m, ar, m0, m1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ range=(ar0, n0, ar1, n1, m) ↔ n0 + m ≤ # ar0 ∧ n1 + m ≤ # ar1 ∧ (∀ n. n < m → ar0[n0 + n] = ar1[n1 + n])
Proof step 3:
⊦ (# ar0 + m) + m1 ≤ #(ar0 + ar1) ∧ m0 + m1 ≤ # ar ∧ (∀ n. n < m1 → (ar0 + ar1)[(# ar0 + m) + n] = ar[m0 + n]) ↔ range=(ar1, m, ar, m0, m1)

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] → [m1, m0, ar, # ar0 + m, ar0 + ar1] flags: <all paths>

Additional information

Used terms: m1, m0, ar, # ar0 + m, ar0 + ar1