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What are the main accomplishments  of Ada Lovelace during this time?
Ada Lovelace was chiefly known for her work on Charles Babbage's proposed mechanical general-purpose computer, the Analytical Engine.
What is noteworthy about the time Ada Lovelace worked on Charles Babbage's Analytical Engine?
Lovelace emphasised the difference between the Analytical Engine and previous calculating machines, particularly its ability to be programmed to solve problems of any complexity.

Question: And how did she proceed with that realization?
Self-contained rewrite: How did Ada Lovelace proceed with the realization that the Analytical Engine could be programme to solve problems of any complexity?