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"slipped further" is correct and usable in written English.
You can use it when you want to describe an action that has gone downhill, or a situation that is becoming worse. For example: "The economy continued to decline, and GDP slipped further."
Exact(60)
Time Warner's stock slipped further.
Meanwhile, her mother's health slipped further.
As Evans grew older, his scholarly standards slipped further.
In a strange way, Zahir's stature grew as his country slipped further into the abyss.
Then, in February, Baptista got injured and in his absence Málaga slipped further from safety.
Schwartzel bogeyed the penultimate hole and slipped further behind with a five at the last.
Towards the end, Cooke writes revealingly that 'the unreality of "the war" slipped further into memory'.
And yet, day by day, that prospect has slipped further out of view.
Defending champion Inter Milan slipped further behind after losing to Parma, 2-0.
Mr. Capo said he did not know whether the student straightened out or slipped further.
In the more comforting surrounds of the club's own television station, his guard slipped further.
Write better and faster with AI suggestions while staying true to your unique style.
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