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Writing a good proposal (including the presentation of relevant previous results) need not clash with dual-anonymous reviews. The goal in this regard is to minimize the chances that the proposing team can be identified, while writing the best possible proposal.
For instance, instead of explicitly stating that some previous results were obtained by the proposing team, which now requests follow up, one could consider writing something along the following lines:
'Previous results [ref. 1] have shown X. We wish to follow up on these discoveries, to learn Y, by doing Z.'
Reference 1 at the end of the proposal might well list the authors of the current proposal, but that need not be obvious to the reviewer.
If there is no published reference (but the analysis of the data has reached the point where it is being used to support the request for follow up observations), then existing unpublished results can certainly be included in the proposal, but without explicit reference to the previous proposal ID/title/PI/Co-Is (e.g., there could be a statement along the lines that 'in previous work being prepared for publication we showed the following:...').