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Proof step 3 from proof mkemparray-append (previous step)

⊦ fill(mkarray(n0), empty) + fill(mkarray(n1), empty) = fill(mkarray(n0 + n1), empty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 5:
⊦ #(fill(mkarray(n0), empty) + fill(mkarray(n1), empty)) = # fill(mkarray(n0 + n1), empty) ∧ (∀ n. n < #(fill(mkarray(n0), empty) + fill(mkarray(n1), empty)) → (fill(mkarray(n0), empty) + fill(mkarray(n1), empty))[n] = fill(mkarray(n0 + n1), empty)[n])

Rule argument

spec: array name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [fill(mkarray(n0 + n1), empty), fill(mkarray(n0), empty) + fill(mkarray(n1), empty)] flags: <all paths>

Additional information

Used terms: fill(mkarray(n0 + n1), empty), fill(mkarray(n0), empty) + fill(mkarray(n1), empty)