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The phrase "are the same then" is correct and usable in written English.
It can be used to indicate that two or more things are equal or identical at a specific point in time or under certain conditions.
Example: "If both solutions yield the same results, we can conclude that they are the same then."
Alternatives: "are identical at that point" or "are equal in that case".
Exact(44)
If these are the same, then the source is on-axis.
If both sides of a constraint are the same, then we simply move on.
If the weapons are the same, then the game is a tie.
If they are the same, then the computation is considered error free.
If under the street and under the sea are the same then he was king of both.
If the two values for are the same, then the knot and control points and are removed and control point is inserted.
Similar(16)
So, in case you see that it's the same, then that's great.
"But that's the same then between Heineken Cup matches and league matches in any country.
If x and y have a moment-generating function, and they're the same, then they have the same distribution.
If the successor of two natural numbers is the same, then the two original numbers are the same.
"It comes along with the territory and as long as I remain the same and my soul is the same, then it's o.k.," she said.
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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