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"lead to the idea" is a correct and usable phrase in written English.
It is often used to show that something has caused an idea or conclusion to be drawn. For example, "The data gathered by the researchers led to the idea that the species is endangered."
Exact(38)
How did working on that book lead to the idea for this one?
These facts lead to the idea that a certain cosmic distribution of the major elements occurs throughout the universe.
And that can lead to the idea that Tamny seems to have embraced: regular shutdowns are the best way to limit not only the size of the federal government but also the scope of obligations we have to one another.
In time, that line of thinking would lead to the idea that quasars and radio galaxies were powered by the gravity of supermassive black holes in the centers of galaxies, a widely held notion today.
Curt Decker, director of the US national disability rights network, has been quoted as saying that the treatment could lead to "the idea that people with disabilities don't have to be kept alive or integrated in society".
Newton's laws of motion and of gravitation and Coulomb's law for the forces between charged particles lead to the idea of energy as a quantity that is conserved in a wide range of phenomena (see below Conservation laws and extremal principles).
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Federally funded research helped lead to the ideas and inventions behind Google and smartphones.
That is what led to the idea of the TED Prize.
Requests from two Manhattan clients led to the idea for the product.
This became generally accepted and led to the idea that development is essentially about institutional change.
Such "nation state terrorism" led to the idea that terrorists were essentially freedom fighters.
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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