Research proof index

Self-log fixed point. The two log layers produced by oa.withQueryLog.withQueryLog agree on every support point: simulating the logging oracle over oa.withQueryLog records exactly the queries that the inner withQueryLog already recorded, since withQueryLog does not add new queries to the underlying OracleComp.

Query-log lookup is the OracleSpec specialization of dependent lookup on PolyFun traces.

Fuelled unrolling commutes with interface transport along a lens: the unrolled query tree of the wrapped machine is the lens-translated unrolled tree. The syntactic (FreeM-level) content of interface wrapping, from which handler-level wrapping laws follow by FreeM.liftM naturality without touching machine states.

Pushforward of PMF.uniformOfFintype α under a map f : α → β whose fibers over the image all have the same cardinality k > 0 is the uniform distribution on the image of f. Useful when f is an affine-linear surjection: every fiber is a translate of the kernel and hence has constant cardinality. The proximity-gap proofs use this to bridge the coeff...

If a non-zero bivariate polynomial f divides a non-zero bivariate polynomial g, then all the coefficients of the quoetient are non-zero. -/ @[grind .] lemma coeff_ne_zero {f q : F[X][Y]} (hg : q * f ≠ 0) : q.coeff ≠ 0 := (ne_zero_iff_coeffs_ne_zero q).1 (quotient_nezero hg) /- If q * f ≠ 0, then the X-degree of q is bounded above by the differen...

There exists a maximal Y-index achieving totalDegree. Above it, total-degree contributions are strictly smaller or the coefficient vanishes.