i think it depends on the context my father told me if i left home , he wouldn't give me any money. i left home with that in mind. here with that in mind means what my father told me.

This can also be used as a transition. I think it would be more likely in speaking, but it certainly could appear in writing. It means that the speaker/writer wants you to think about what he just said/wrote as you look at his new information. Or, he came to a conclusion based on some older information. He wants you to see the connection. A businessman might be giving a talk at a meeting. "Last year we saw lower profits resulting from sudden drop in sales. We looked at the data, which showed that, although we had the same number of customers, each customer put in fewer orders. With that in mind, we decided to develop a two-pronged approach to increasing sales: 1) getting our regular customers interested in new products and 2) expanding our customer base by selling in the more rural areas, areas which we have ignored up till now."

with that in mind= while thinking about someone or something Examples: We moved here with the children’s schooling in mind. This room was designed with Carol in mind. With that in mind, let us turn to page 77.

以此为前提 有言在先 something somebody did before