In the sentence you are asking about, 'subject to their being' could simply be replaced with 'if'. So, it will be easy to move the books if there are enough helpers. I hope this helps, Richard

'If' and 'subject to' can both be used to express the conditional. However, they require different grammar. I assume you're already familiar with the 'if' form, but for ease of comparison, here is the basic 'if' structure: If + subject + verb (+ object), (then) subject + verb + (object) And of course, you can invert the two phrases (without 'then'). She will be happy, if she eats cake. If the shareholders agree, then the companies will merge. The equivalent sentences using 'subject to' are: She will be happy, subject to her eating cake. Subject to the shareholders' agreement, the companies will merge (note: no 'then'). What's going on here? Each of the phrases following 'subject to' is a noun phrase. The latter example is probably easiest to understand; the verb 'agree' has been converted into a noun, and 'shareholders' has become possessive. In the first example, we also have a possessive; 'she' has become 'her'. And 'eating cake', while it looks like a verb and a noun, behaves like a single noun. It is the act (abstract noun) of eating a cake. You wouldn't have to use a possessive after 'subject to'. In my examples, I could alternatively say 'subject to the cake being eaten by her', or 'subject to an agreement being reached between the shareholders'. But phrasings like these are a lot more verbose, potentially confusing even to L1 speakers, and can come across as pretentious. And of course, there is no possessive in the original example. 'There being' simply behaves as a noun equivalent to 'there are'. You could also say 'subject to the existence of enough helpers'. This would be grammatically correct. The meaning would be clear. But it would sound odd. One more difference between 'if' and 'subject to' is the appropriate context. 'If' is fine in practically any context. 'Subject to' is rarer. We find it in academia, business, law, and other formal contexts. We don't generally use it with friends, family or the average colleague.

Hi Bianca, Other answers have given good explanations, but it might also help to think of that as being similar to the Spanish verb haber. Except in English it’s almost as if we need to say it twice in that use. There acts as a sort of helper in English that sometimes comes before words meaning to be or to exist. Other examples: There are There exists

'subject to there being' is the same as 'subject to there existing', or 'as long as there are' "... subject to there existing enough helpers". "...as long as there are enough helpers".

I hope this clears it up for you, not entirely sure what you're asking but I hope this makes it clear: The phrase subject to, means if this condition is met. So you can say, "subject to answering this question correctly" or "subject to the regulations changing"; however, colloquially this phrase is only used in very formal documents just to clarify. You can use it in everyday speech but people would find your phrasing cold and abrasive (native speakers anyway). The next part, the "there being", is just exactly that. Subject to "this thing existing", so in this case above the existence of enough helpers. There could be enough helpers or there could not be. To put it another way, you could say, "We are restricted by the fact that there could not be enough helpers." So, subject to + there being enough helpers = moving all the books should not take long. I hope this answers your question!