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Discover Ludwig"let us proceed with" is a perfectly valid expression in written English.
You can use it when you and one or more other people are beginning or continuing an activity together. For example, "Let us proceed with our plan to remodel the kitchen."
Exact(7)
Let us proceed with (2.35).
Let us proceed with the programme," he said.
Let us proceed with the proof of (ii).
Now let us proceed with our main objective of defining the semigroup representation on (widetilde{mathrm {H}}(W^s)).
Let us proceed with care.
Let us proceed with the task of identifying the particular groups of genes, which display significant differences in the intragene methylation profiles between the cell types.
Similar(53)
Then I talked my boss into letting us proceed with this with a reasonable budget.
Let us proceed further with describing the possible states of the overall system.
Let us proceed in accordance with our nation's traditional moral compass, yes, but in a manner that is fair and at a pace that is deliberate and responsible.
"Let us proceed to deal calmly and quietly with the court's decision," Mr Iloilo said in a televised address.
Let us then, Mr. President, if other countries cannot supply an adequate example, let us proceed upon our own principles, and with the great end of government in view, the happiness of the people, it will be strange if we err.
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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