Update internationalization documentation

docs/source/internationalization.md

@@ -1,18 +1,38 @@
 # Internationalization
 
-This package supports the following languages specified in `conf.py` using the  `language` option:
-
-- ar
-- cs
-- de
-- es
-- fr
-- it
-- ja
-- nl
-- ru
-- zh_CN
-
-```{note} Work in progress
-Not all languages listed above are support across all admonition types
+This package supports **33 languages** for all proof directive types. Translations are specified in `conf.py` using the `language` option.
+
+## Supported Languages
+
+All 15 directive types (Algorithm, Assumption, Axiom, Conjecture, Corollary, Criterion, Definition, Example, Lemma, Notation, Observation, Property, Proposition, Remark, Theorem) have complete translations in the following languages:
+
+| Language | Code | Language | Code |
+|----------|------|----------|------|
+| Arabic | `ar` | Bengali | `bn` |
+| Bulgarian | `bg` | Chinese | `zh_CN` |
+| Czech | `cs` | Danish | `da` |
+| Dutch | `nl` | Finnish | `fi` |
+| French | `fr` | German | `de` |
+| Greek | `el` | Hebrew | `he` |
+| Hindi | `hi` | Hungarian | `hu` |
+| Indonesian | `id` | Italian | `it` |
+| Japanese | `ja` | Korean | `ko` |
+| Malay | `ms` | Norwegian | `no` |
+| Persian | `fa` | Polish | `pl` |
+| Portuguese | `pt` | Romanian | `ro` |
+| Russian | `ru` | Spanish | `es` |
+| Swedish | `sv` | Thai | `th` |
+| Turkish | `tr` | Ukrainian | `uk` |
+| Urdu | `ur` | Vietnamese | `vi` |
+
+## Usage
+
+To use a specific language, set the `language` option in your Sphinx `conf.py`:
+
+```python
+language = 'es'  # For Spanish
 ```
+
+If no language is specified, **English** (`en`) is used as the default.
+
+All proof directives will automatically use the appropriate translations for the selected language.