Can you tell me which word is equivalent to providing in this sentence below, if or in case?
The deposit is refundable when you leave, providing you haven’t damaged anything.
In OP’s context, providing is equivalent to if (it can validly be replaced by if, but not by in case).
If some statement S depends on the hypothetical scenario X being true (or false, as in not X or !X)…
S [is true/will happen] if X
S providing X
S so long as X
S as long as X
S unless (!X)
Note that OP’s “hypothetical” is already negated (you have not damaged anything). If we remove the negation, it becomes !X, so an equivalent to OP’s statement would be…
The deposit is refundable when you leave, unless you have damaged anything.
If some action A is only being taken to avoid the possibility of X being true (or to deal with issues that will only arise if X is in fact true)…
A lest X
A in case X
Don’t damage anything, lest you lose your deposit.
We ask for a deposit in case you damage anything.
Source : Link , Question Author : Truong Ha , Answer Author : FumbleFingers