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Discover Ludwig"next higher" is correct and can be used in written English.
You can use it when you want to refer to something which is at a higher level or order than what has already been mentioned. For example, "This year's model has more features than the previous model. The next higher model includes even more features."
Exact(59)
Both were cooked to the next higher degree of doneness.
The C above middle C is shown as c″, and the next higher C as c‴.
"Deity" signifies the upper goal, the next higher level toward which the cosmic order spontaneously tends.
When they are wiped out, the losses move to the next higher tranche.
Because the closest shell is filled, the third electron goes into the next higher shell.
Could the Jayhawks be the next higher seed to fall to N.C.
It then becomes a nucleus of the next higher element in the periodic table of the elements.
The distal barbules bear tiny hooklets (hamuli) that fit into grooves on the proximal barbules of the next higher barb.
Ri is transposed to become the left-hand part of the next higher intermediate cipher, Li + 1.
In the next higher order of (epsilon), Eqs.
Comparisons to its next higher and lower methyl esters are also presented.
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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