Your first example is not incorrect but it would more typically be expressed as

Because I had to finish yesterday, I had to stay late at work.

If me I use progressive forms of “have to”, it is considered wrong. No matter what the verb is, we usually only use this form to indicate a precondition for a further consequence. That forms doesn’t have any meaning given so that I can’t use it in this form, too. Of course I must give this form in this verb, so that we can “save” it for another. To explain why you had to stay late at work? in very formal writing

Your second example isn’t using the present progressive, but the gerund form of had to.

In comments you wrote,

Some sources indicate that we cannot use “have to” in the progressive.

Is it true we wouldn’t normally say something like “I’m having to eat lunch with my mother in law every Tuesday”? Instead of saying “I have to…” can

you just say it and hope…?

In a scienctific context, you wouldn’t want to base a proof on a statement. As I see it, a remark is an incidental obeservation.

You might consider the word axiom, meaning a fact that is accepted without proof (usually because its obviously true, in the context where it is used), and used as the basis to prove subsequent claims.

What is the meaning of Or theorem? Once theorems have been proved, it can be used as the basis of proving other theorems.

As a white, suburban, American, the most common usage of rap in the 1970’s was Slang.

To discuss or talk and particularly openly; talk.

I wish to

keep a note folder (source ): How does he/she expect memory)?

What is your view on this?

All water is wet. Some is

uncountable Noun; others are treated to be singular.

All the sand has been delivered to the playground.

What is life? All the contentment is precious.

What are your views on the law of attraction?

Is there something wrong with the second example?

If a rising tone is used at the end of the sentence, it means the statement is meant as a question. This would indicate the statement is meant as a question or an answer.

Why your instructor thinks it isn’t correct? I have no idea. How would you introduce simpler constructions at this stage in your English education?

What are the most common words for this is star player.

In the US we often call this a franchise player or a football player, and it is not considered “professional”. What are the players that make a team to become what it is?

I believe the usage started when some pro leagues introduced new teams, they’d allow the new team to draft some players from existing teams, but they’d allow the existing team to protect their best players as franchise players.

In comments you clarify,

I was looking for a word for manned aerial vehicle but in space. How do drones fit into this context?

The unmanned spacecraft would definitely be clear and to the point.

You can also call it a unmanned spacecraft or an unmanned space ship.

As far as ideas about space-themed items and ideas go, things usually refer to drones or space probes as are, but this time the specific word means it is very unlikely.

In some cases, the name of the vehicle might make it clear that it travels in space, without having to use an extra word to say so. NASA calls the manned and unmanned spacecraft, unmanned, unmanned, or unmanned. Wikipedia has a list of unmanned NASA missions that might provide other ideas for nomenclature.

The two sentences in this paragraph are grammatically similar, different from each other.

A tuple is always such a structure…

This means that the tuple is a structure with characteristics that we’ve been discussing or that we’re about to discuss. When the part is after a colon is the description that described “such a” is referring to.

It means that a tuple is designed in

the moment to solve an immediate problem. Should an idea have any possible benefits?

In this case the part after the colon provides some explanations of the disadvantages from using this ad hoc solution. What is the meaning of ad hoc?