What does the phrase "reduce the contract in writing" mean?
Could anyone (native English speaker) help me, please, and explain what the phrase "reduce the contract in writing" means? Does it mean that the Parties decided to enter into the Contract, because they came to an agreement to do smth?

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It means to spell out (say) the terms of the contract.  Reduce to writing means put in writing all of the details of the contract.

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I've never heard the phrase "reduce the contract to writing" exactly we usually say "put it in writing". Like an agreement/decision has been made so now lets make it official and put it into a written record/contract. Hope that helps.

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Sorry, I have used a wrong preposition, the phrase is as follows "reduce the contract in writing".