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Related to type up: have over, could do with
type something up
to type a handwritten document; to type a document, perhaps using a computer. I will give this to you as soon as I type it up. Please type up this document.
1. To compose a finished document from some set of notes by typing: I hired an assistant to type up my handwritten letters. The secretary typed the handwritten notes up.
2. To draft some kind of document by typing: We sat up all night typing up a charter for the organization. Do you have time to type a few letters up for me?