Three Statement Linking Question - Gain on Sale of PP&E

I've been taught that if there's a gain on sale of PP&E, on cash flow statement, I should subtract the gain from cash from operations and show the full amount of proceeds (book value + gain) in cash from investing activities.

However, when it comes to linking the three statements in financial modeling, it is typical to first forecast the sale of PP&E on cash flow statement, and then link it back to balance sheet by taking PP&E on balance sheet and subtract the proceeds from sale of PP&E on cash flow statement.

Wouldn't this cause a problem if somehow the sale of PP&E yields a gain? Wouldn't we subtract more than book value from the PP&E on balance sheet? Should we account for this by linking the subtracted gain in cash from operations as well by adding it to PP&E on balance sheet?

Just a thought coming from a confused student when linking statements. Would appreciate any help. Thanks.

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