Research proof index

Let $f: G \to G'$ be a function, and let $S$ denote the set $S := \{ f(x+y)-f(x)-f(y): x,y \in G \}.$ Then there exists a homomorphism $\phi: G \to G'$ such that $|\{f(x) - \phi(x)\}| \leq |S|^{10}.$

A symmetry identity in the $\tau$-minimizer endgame. Let $X_1',X_2'$ be independent copies of $X_1,X_2$, and set $U=X_1+X_2$, $V=X_1'+X_2$, $W=X_1'+X_1$, and $S=X_1+X_2+X_1'+X_2'$. Then the conditional mutual informations agree: $I[V:W\mid S]=I[U:W\mid S]$.

If the set is inf-closed, elements of countablInfClosure can be written as countable intersections of antitone sequences of sets.

The set of large left jump times has no accumulation points. TODO: maybe to_dual can be extended to simplify this proof as the proof of the second part is very similar to the first part.

Transport a compact system along an equivalence of types.

The set of Finset coercions forms a compact system.