I am grad student working in an engineering field that heavily uses math (we have theorems and proofs in our papers). One of the theorems I was working on had a proof that goes something like this: since X=Y+Z, we can write Y=X-Z. The issue is this true if both Y and Z are finite (Y,Z are non-negative here), and I had not shown it. My entire work was built upon proof of this theorem. After spending about a month of sleepless nights and dark thoughts I could finally prove the finiteness of quantities involved and salvage the paper.