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Proof step 18 from proof append-inj (previous step)

# ar = # ar2, # ar0 = # ar1, ∀ n. n < # ar1 + # ar2 → (ar0 + ar)[n] = (ar1 + ar2)[n] ⊦ ar = ar2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 20:
# ar0 = # ar1, # ar = # ar2, ∀ n. n < # ar1 + # ar2 → (ar0 + ar)[n] = (ar1 + ar2)[n] ⊦ # ar = # ar2 ∧ (∀ n. n < # ar → ar[n] = ar2[n])

Rule argument

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

Additional information

Used terms: ar2, ar