How to prove that carbon dioxide is necessary for the process of photosynthesis?

You can experiment. It is necessary to place the plant under a sealed hood and supply only a mixture of gases without the presence of carbon dioxide. The photosynthesis process will be stopped. But this is quite difficult to implement. It is much easier to fill a flask with carbon dioxide by simply leaving a burning candle there. Photosynthesis will be more intense. But we will need to examine the cells under a microscope and carry out an experiment with several samples for a long time, since a scientific approach has to be applied.