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The phrase "the contrary when" is not correct and does not convey a clear meaning in written English.
It seems to be an incomplete expression that may be intended to contrast two ideas or situations, but it lacks clarity and context. Example: "The results were not as expected; in fact, the contrary when we analyzed the data further."
Exact(60)
But a new study offers evidence to the contrary when it comes to cardiovascular disease.
On the contrary, when others bear the costs of mistakes, the incentives favour self-delusion.
On the contrary, when I've seen the president-elect and Laura, they couldn't be warmer.
On the contrary, when we bumped into each other we liked to make each other laugh.
On the contrary, when too many cars pursue too few customers, consumers are sure to benefit.
It is quite the contrary when Westwood is playing for himself.
"On the contrary, when you are with him, you feel that you even want to protect him.
On the contrary, when we have.
On the contrary, when one has.
Plato, on the contrary, when explaining the physical world, never got lost in a detailed examination.
On the contrary, when the polarization per unit volume is plotted, the trend is reversed.
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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