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The phrase "a further demonstration of" is correct and usable in written English.
It can be used when you want to indicate an additional example or proof of something that has already been mentioned or established.
Example: "The recent study serves as a further demonstration of the effectiveness of the new teaching methods."
Alternatives: "an additional example of" or "a continued illustration of".
Exact(45)
The use of his cells in making mice walk is a further demonstration of their versatility.
"This measure is a further demonstration of how the UK takes its international environmental responsibilities seriously".
All the finale brought was late false hope and a further demonstration of Liverpool's enduring reliance on their captain.
"It's a further demonstration of our core strategy of 'national brands delivered locally', and it's very important to us.
This is acting of the highest order, and the film is a further demonstration of Mike Leigh's unsentimental compassion.
But there was more to an ultimately comfortable victory over Stoke City than a further demonstration of the ruthless efficiency that Jürgen Klopp has created at Anfield.
Similar(14)
Illustrative examples give a further demonstration for the effectiveness of the proposed neural network.
A further demonstration case of the co-sintering of two particles of different sizes is provided.
Even in a season when he has often borne the brunt of fan frustration, this was a new experience for Kean, with a further demonstration involving hundreds of supporters taking place after the final whistle.
Pinot had been prominent throughout the closing stages and outsprinted Froome to the line in a further demonstration that an era of almost unrelieved bleakness for France, which began when Hinault won his last Tour in 1985, may be coming to an end.
Firstly, it is a yet further demonstration of the refusal of successive British governments to do deals with terrorists and hostage takers.
More suggestions(15)
a further evidence of
a further test of
a further outbreak of
a further stage of
a further manifestation of
a further trial of
a further expression of
a supplementary demonstration of
a further proof of
a further sign of
a further deterioration of
a further postponment of
a further piece of
a further £750m of
a further dimension of
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com