The phrase "reinforcing the notion" is both correct and commonly used in written English.
You can use it when you want to express that something is strengthening or supporting a particular idea or concept. Example: The latest studies on climate change are reinforcing the notion that immediate action is necessary to prevent disastrous consequences.
"We are rapidly reinforcing the notion that we are a nation of jailers - we constantly incarcerate the Aboriginal people".
Its 1998 income was $307 million, reinforcing the notion that an Englishman's home really is his castle, if vicariously.
In short order, Notre Dame dispatched Army, 12-6, thus reinforcing the notion that Rockne's oratory had worked magic.
Reinforcing the notion of a Chinese revival are what appear to be murals celebrating Chinese culture scattered throughout the site, such as those depicted in Figure 9 below.
Everyone is an employee, but by using this word are we (unconsciously) reinforcing the notion that there is some difference between management employees and others?
It even helped to forge a sense of national identity by reinforcing the notion that Americans were a chosen people, beneficiaries of God's special grace.
So much effort goes into reinforcing the notion of teamwork and camaraderie that there wasn't a trace of the sniffy competitiveness you often get at these things.
But these moves did not stop the stock's steep downward spiral, reinforcing the notion that Bear would benefit from a change in leadership.
Such blanket restrictions based on nationality alone are counterproductive, reinforcing the notion that America is hostile to Islam in general, not just protecting itself against terrorism.
He won major victories in the 1949 and 1953 federal elections, reinforcing the notion that the Liberals were destined to govern Canada forever.
Those millions can be spent on arresting, well-produced adverts reinforcing the notion of Britain being great again and far better off without the shackles of Brussels.
