The phrase "increasingly realized that" is grammatically correct and can be used in written English.
You can use this phrase when you want to express that someone has come to understand or comprehend something gradually over time. For example: "I increasingly realized that my job was not fulfilling me, so I started looking for new opportunities." "Over the course of our relationship, I increasingly realized that we had different goals and values." "As I grew older, I increasingly realized that my parents were right about many things." "In my research, I increasingly realized the importance of including diverse perspectives."
"All of those nations have increasingly realized that terrorism is a danger to each and every one of us," Secretary Powell said.
And as the stars filmed more of this season's episodes, they increasingly realized that they did not want to give up quite yet a job that provided so much fun -- and remuneration.
As Lehman tried to make a case with the media and regulators that investors betting against its stock were unfairly going after the firm, top executives increasingly realized that their strategy was failing and assets were withering.
As he and Singapore mellowed and became steadily more tolerant, open and democratic, Lee increasingly realized that he could trust Singaporeans to make decisions on their own, and he is one of the few Confucian emperors ever to step down voluntarily.
On the other hand, it is increasingly realized that glucose electrooxidation is sensitive to surface structure of the electrocatalyst.
Furthermore, it has been increasingly realized that the needed AC information may be derived from multiple sources used together: emission data, partial transmission data, and segmented MR images, for example [15, 16].
As NIEHS director, I increasingly realize that, as the writer André Gide said, "The most important things to say are those which often I did not think necessary for me to say because they were too obvious".
Perhaps more significant, employers are increasingly realizing that they need to listen to and act on workers' demands if they want a stable and productive work force.
But as scenes flash by of Pippa's tumultuous youth, you increasingly realize that she is going through the motions of domestic bliss.
But, as Professor Conley added, companies are increasingly realizing that employees need to be disconnected from time to time and that "giving workers time to chill helps ultimate long-term productivity".
