Initial segments exist

There's no statement right now saying
```lean
example (k r : ℕ) :
∃ (𝒞 : finset (finset ℕ)), is_init_seg_of_colex 𝒞 r ∧ 𝒞.card = k := sorry
```
It would be nice to show we have initial segments of colex of any length (in particular in conjunction with #1).
Alternatively, this could have `𝒞 : finset (finset (fin n))`:
```lean
example {k r n : ℕ} (h : k ≤ choose n r) :
∃ (𝒞 : finset (finset (fin n))), is_init_seg_of_colex 𝒞 r ∧ 𝒞.card = k := sorry
```
(Could also be a definition instead of a proof of `∃`, this would let us evaluate the smallest shadow size in an explicit way compared to #2).

The issue gives no file or test path. Start by locating is_init_seg_of_colex and reviewing the related work in #1 and #2; decide whether the result should be an existential theorem or an explicit definition. Done means the chosen statement is present and established for the stated bounds.

Written by the indexing model from the issue text.