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The phrase "have mutually stimulated" is grammatically correct and can be used in written English.
It means that two things or ideas have influenced or motivated each other in a positive way. Example: The collaboration between the two scientists have mutually stimulated new research ideas and led to groundbreaking discoveries.
Exact(1)
These developments have mutually stimulated the fields of analytical chemistry and biotechnology.
Similar(58)
However, "tensions" had arisen and they had mutually agreed on a separation.
This means having mutually and jointly guaranteed deposit insurance.
Tourism has been stimulated by Baron von Falz-Fein.
This complete world has always stimulated me.
α-melanophore-stimulating hormone (α-MSH) and melanin-concentrating hormone (MCH) appear to have mutually antagonistic effects on melanophores, with α-MSH enhancing melanin and melanophore development, and MCH promoting aggregation of melanosomes and downregulating secretion of α-MSH [46] [49].
Indeed, the two leaders have mutually reinforcing goals.
"We have mutually decided to part ways," he said.
These must have mutually agreed objectives and timescales.
The #49ers and Jim Harbaugh have mutually agreed to part ways.
All this has stimulated a construction boom.
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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