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"further suppose that" is a perfectly valid phrase in written English.
It can be used to introduce a hypothetical situation that is additional to one already established. For example, "Further suppose that the weather is cold in addition to the fact that there is six feet of snow on the ground."
Exact(58)
Further, suppose that (3.26). is univalent in and.
Further, suppose that is equicontinuous on for any Then is relatively compact.
Further, suppose that satisfies NST-condition (I) with T. Define a sequence in by the following algorithm: (3.25).
Further, suppose that satisfies NST-condition (I) and (III) with T. Define a sequence in by the following algorithm: (3.1).
Then further suppose that it somehow survives the inevitable court challenge.
Further, suppose that (H1 - H3) are satisfied.
Further, suppose that (A_{0}) is nonempty.
Further suppose that (delta<|g^{delta}|).
Further suppose that spectrum inversion does not in fact occur.
Further, suppose that (H1 - H2) and (H4) are satisfied.
Further suppose that (k_{1} y)) admits compact support.
More suggestions(17)
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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