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Proof step 8 from proof mkemparray-append (previous step)

n < n0 + n1 ⊦ (fill(mkarray(n0), empty) + fill(mkarray(n1), empty))[n] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ n < # ar0 + # ar1 → (ar0 + ar1)[n] = (n < # ar0 ⊃ ar0[n];ar1[n - # ar0])
Proof step 10:
n < n0 + n1, n < # fill(mkarray(n0), empty) + # fill(mkarray(n1), empty) ⊦ (n < # fill(mkarray(n0), empty) ⊃ fill(mkarray(n0), empty)[n];fill(mkarray(n1), empty)[n - # fill(mkarray(n0), empty)]) = empty

Rule argument

spec: <toplevel> name: append-at seq: ⊦ n < # ar0 + # ar1 → (ar0 + ar1)[n] = (n < # ar0 ⊃ ar0[n];ar1[n - # ar0]) subst: [n, ar1, ar0] → [n, fill(mkarray(n1), empty), fill(mkarray(n0), empty)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # fill(ar, a) = # ar; (s)% ⊦ # mkarray(n) = n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n, fill(mkarray(n1), empty), fill(mkarray(n0), empty)