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Proof step 7 from proof subarray-split-size (previous step)

⊦ copy(ar, n, mkarray(n0 + n1), 0, n0 + n1) = copy(ar, n, mkarray(n0), 0, n0) + copy(ar, n + n0, mkarray(n1), 0, n1)

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:
⊦ # copy(ar, n, mkarray(n0 + n1), 0, n0 + n1) = #(copy(ar, n, mkarray(n0), 0, n0) + copy(ar, n + n0, mkarray(n1), 0, n1)) ∧ (∀ n2. n2 < # copy(ar, n, mkarray(n0 + n1), 0, n0 + n1) → copy(ar, n, mkarray(n0 + n1), 0, n0 + n1)[n2] = (copy(ar, n, mkarray(n0), 0, n0) + copy(ar, n + n0, mkarray(n1), 0, n1))[n2])

Rule argument

spec: array name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [ copy(ar, n, mkarray(n0), 0, n0) + copy(ar, n + n0, mkarray(n1), 0, n1), copy(ar, n, mkarray(n0 + n1), 0, n0 + n1)] flags: <all paths>

Additional information

Used terms: copy(ar, n, mkarray(n0), 0, n0) + copy(ar, n + n0, mkarray(n1), 0, n1), copy(ar, n, mkarray(n0 + n1), 0, n0 + n1)