chore: lemmas about BEq on List String.Slice

[TwoFX]

This PR adds lemmas about BEq on List String.Slice.

We show (l == l') = false ↔ l.map copy ≠ l'.map copy and deduce a BEq version of the theorem about "intercalate-then-split":

theorem toList_split_intercalate_beq {c : Char} {l : List String} (hl : ∀ s ∈ l, c ∉ s.toList) :
    ((String.intercalate (String.singleton c) l).split c).toList ==
      if l = [] then ["".toSlice] else l.map String.toSlice

[mathlib-lean-pr-testing]

Mathlib CI status (docs):

• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase fcdd9d1ae821497aeaedaae9bfd94f976d538d35 --onto 4bf7fa7447eea00cecba8327bb9c9e5f4485f0a7. You can force Mathlib CI using the force-mathlib-ci label. (2026-03-23 14:13:01)

[leanprover-bot]

Reference manual CI status:

• ❗ Reference manual CI will not be attempted unless your PR branches off the nightly-with-manual branch. Try git rebase fcdd9d1ae821497aeaedaae9bfd94f976d538d35 --onto cfa8c5a036d6990635c6ec50b02d0e806995cec3. You can force reference manual CI using the force-manual-ci label. (2026-03-23 14:13:03)