The phrase "after demonstrating how" is correct and usable in written English.
It can be used when you want to indicate that something follows a demonstration or explanation of a process or method.
Example: "After demonstrating how to assemble the furniture, the instructor allowed the participants to try it themselves."
Alternatives: "following the demonstration of" or "subsequent to showing how".
After demonstrating how neural decoding can be used to read out what places are covertly replayed in the brain, the team began a series of technical innovations that progressively improved the field's ability to accurately decode how the brain represents place both during navigation and in sleep or rest.
After demonstrating how to "tap" the magazine into place in the handle and "rack" a round into the chamber with a quick pinch-pull on the back of the sliding frame, Mr. Mastroianni showed me how to clasp the gun in my right hand (finger along the barrel off the trigger), filling in space on the handle with my left hand, meshing the fingers in a steadying grip.
After demonstrating how MIDMRA work, we now provide analysis on the optimization and time complexity of this algorithm.
"We hope these beauty tips will help you carry on with your daily life," the host suggests after demonstrating how to mask the signs of violence.
After demonstrating how thoughts like "I'm not good enough to do that job" or "I'll probably let the team down" can dilute our confidence at an alarming rate, I could then segue into ways to change those false outlooks and inspire folks to build their confidence muscles.
"These antigay remarks, coming so soon after, demonstrate how much needs to be done".
Building codes don't require safe rooms, despite years of research (and vivid examples after disasters) demonstrating how a few thousand dollars can save lives.
Hal Varian, Google's chief economist, co-authored a paper shortly after the financial crisis, demonstrating how Google Trends, which aggregates search volume for specific words or phrases, can accurately forecast unemployment claims, a key economic indicator which is released weekly by the Department of Labor.
"The difference between excellence and mediocrity is subtle," she says, after a day spent demonstrating how to make tortillas.
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Less than 12 months after Kim wrote that piece, demonstrating how much 'brand' matters, four universities formerly in the 1994 Group joined the Russell Group.
