Finding a Minimal set that statisfy some property

Stream: Is there code for X?

[ym]

Hi, i am new and its my first time writing here so hope it is the right place. Let m:ℕ be some number and let have some property P of subsets of {1,...,m} (P:Set (Fin m) → Prop) . I know that the full set satisfy P and want to find a minimal set that satisfy this property, is there a simple way to do this?
For context, I try to formulate the basics of min-entropy and density (from "Rectangles are nonnegative juntas") and specifically I need this for defining density restoration (Proposition 3.6. in "QUERY-TO-COMMUNICATION LIFTING USING
LOW-DISCREPANCY GADGETS").

[Kevin Buzzard]

Can you write the statement of what you want in Lean as a #mwe ? That's the way we encourage people to ask questions here. Click on the link for more details. Questions from new members usually go in #new members but I think your question is fine here.