La pruvo montras ke la informo estas vera.

La is Esperanto’s definite article, equivalent to English the. It is used when the speaker means a specific proof and a specific piece/body of information.

Esperanto has only one article: la. It does not have separate words for a or an.

These endings show the part of speech:

• pruvo, informo → -o = noun
• montras, estas → -as = present-tense verb
• vera → -a = adjective

This is one of Esperanto’s most regular features: the ending gives you a lot of grammatical information right away.

Ke means that and introduces a subordinate clause:

• ke la informo estas vera = that the information is true

After verbs like montri (to show), diri (to say), scii (to know), and pensi (to think), Esperanto commonly uses ke to introduce the content of the statement.

Usually, no. In English, you can often say The proof shows the information is true without that. In Esperanto, you normally keep ke:

• La pruvo montras ke la informo estas vera.

Leaving it out would sound unnatural or unclear to most learners and speakers.

Because la informo is the subject of the clause la informo estas vera.

A native English speaker may expect it to be the object of montras, but in Esperanto the thing being shown is actually the whole clause:

• ke la informo estas vera

So the structure is basically:

• The proof shows [that the information is true].

Inside that subordinate clause:

• la informo = subject
• estas = verb
• vera = predicate adjective

That is why informo does not take -n.

Because vera is not a direct object. It is a predicate adjective after estas.

In Esperanto, adjectives used after esti usually just describe the subject:

• la informo estas vera = the information is true

Since la informo is singular, the adjective is also singular: vera.

Compare:

• La informo estas vera.
• La informoj estas veraj.

Yes, informo is singular.

This can feel a little different from English, because English information is usually uncountable. In Esperanto, informo is a normal noun and can refer to information as a unit, a piece of information, or information in a general sense, depending on context.

If you want the plural, you can say informoj.

Yes. It is a full subordinate clause functioning as the content of montras.

You can think of it as the answer to What does the proof show?

Answer:

• ke la informo estas vera

So even though montras is followed by several words, those words belong together as one clause.

Yes, Esperanto word order is fairly flexible, but the given order is the most neutral and natural:

• La pruvo montras ke la informo estas vera.

A different order is possible for emphasis, for example:

• Ke la informo estas vera, montras la pruvo.

That is grammatical, but it is more marked and less basic for a learner.

Both styles are seen:

• La pruvo montras ke la informo estas vera.
• La pruvo montras, ke la informo estas vera.

Many writers do put a comma before ke, especially when introducing a subordinate clause, but Esperanto punctuation is not completely rigid here. The version without the comma is also acceptable.