In Fact Meaning

(idiomatic, modal) Actually, in truth.

Example:   People think tomatoes are vegetables, but, in fact, they are fruits.‎
1898, Winston Churchill, chapter 3, The Celebrity:
  Now all this was very fine, but not at all in keeping with the Celebrity's character as I had come to conceive it. The idea that adulation ever cloyed on him was ludicrous in itself. In fact I thought the whole story fishy, and came very near to saying so.
1915, Mrs. Belloc Lowndes, The Lodger, chapter I:
  A great bargain also had been the excellent Axminster carpet which covered the floor; as, again, the arm-chair in which Bunting now sat forward, staring into the dull, small fire. In fact, that arm-chair had been an extravagance of Mrs. Bunting. She had wanted her husband to be comfortable after the day's work was done, and she had paid thirty-seven shillings for the chair.
2015 August 8, Bob Holmes, Ocean hills yield secret ecosystems, New Scientist, Issue 3033, page 14,
  We tend to think of the seafloor a few kilometres down as a flat plain. In fact, about two-thirds of this “abyssal” seabed is made up of gentle rolling hills a few hundred metres high, says Jennifer Durden at the University of Southampton, UK.