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Proof step 7 from proof append-eq-left (previous step)

# ar0 = # ar1, ∀ n. n < # ar + # ar1 → (ar + ar0)[n] = (ar + ar1)[n] ⊦ ar0 = ar1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 9:
# ar0 = # ar1, ∀ n. n < # ar + # ar1 → (ar + ar0)[n] = (ar + ar1)[n] ⊦ # ar0 = # ar1 ∧ (∀ n. n < # ar0 → ar0[n] = ar1[n])

Rule argument

spec: array name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [ar1, ar0] flags: <all paths>

Additional information

Used terms: ar1, ar0