setting off an "if" clause

[Harry_Ph]

Please advise if the "if" clauses in items 1 and 2 should be set off with commas, i.e., commas after "that," and kindly provide explanations why there should be commas or no commas after "that." To me, in item 1, a comma should not be provided after "that" because the "if" clause is directly related to the following "then" clause. In addition, in item 2, I am more convinced that a comma should not be provided after "that," although it seems fine as well to have a comma after "that" (which some authors insist). Here are the examples:

1) We see that if X has n nodes, then R provides the strongest connection.

2) We note that if F is a fuzzy subset of X, we can make statements similar to the previous ones.

I will appreciate if somebody can provide explanations and feedback on these issues.
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The more we learn, the less we seem to know.

[Mister Micawber]

No comma after 'that'. No comma between conjunction and clause unless the subclause is non-restrictive.
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Native English teacher at Mister Micawber's

[Harry_Ph]

I see. But some insist that the "if F is a fuzzy subset of X" in item 2 is just an intervening clause. Is that acceptable, Mister Micawber? If that is possible, what is still the best rule to be followed in this context?
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The more we learn, the less we seem to know.

[Harry_Ph]

And our subclauses here are the "if" clauses, right?
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The more we learn, the less we seem to know.

[Harry_Ph]

I already found the answer in the Chicago Manual of Style. Thanks for the input, Mister Micawber.
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The more we learn, the less we seem to know.

[Esl_Expert]

Hello Harry,

What did you find in the Chicago Manual of Style?

It seems to me that using a comma after the word "that" would basically result in making the IF-clause "extra information" (i.e. non-essential) in the sentence. In other words, an additional comma would tend to make the IF-clause parenthetical.

So, my take on your question is the same as MM's.
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“Nature hides her secrets because of her essential loftiness, but not by means of ruse.” ~ Albert Einstein

[Harry_Ph]

Hi, Esl_Expert. The Chicago Manual of Style states that when two conjunctions appear next to each other, they should not be separated by a comma if there would be no pause between them if they were spoken aloud—or, in grammatical terms, if the dependent clause is restrictive in meaning.
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The more we learn, the less we seem to know.