Research proof index

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.

The Physicists Hermite polynomial are defined as polynomials over ℤ in X recursively with physHermite 0 = 1 and physHermite (n + 1) = 2 • X * physHermite n - derivative (physHermite n). This polynomial will often be cast as a function ℝ → ℝ by evaluating the polynomial at X. -/ noncomputable def physHermite : ℕ → Polynomial ℤ | 0 => 1 | n + 1...

Given a list i :: l the left-most minimal position a of i :: l wrt r as an element of Fin (insertionSortDropMinPos r i l).length.succ. -/ def insertionSortMinPosFin {α : Type} (r : α → α → Prop) [DecidableRel r] (i : α) (l : List α) : Fin (insertionSortDropMinPos r i l).length.succ := ⟨insertionSortMinPos r i l, insertionSortMin_lt_length_succ r...

Closed form for the iterated derivatives of the resolvent: the n-th derivative is (-1)ⁿ · n! · (resolvent z)ⁿ⁺¹.

The single-term coordinate chain rule for a holomorphic outer g, anti-holomorphic version, pointwise at u: ∂̄_I (g ∘ f) = deriv g (f u) · ∂̄_I f. As in dWirtingerCoord_comp_holomorphic_apply, the ∂g/∂f̄ channel vanishes and ∂g/∂f collapses to deriv g (f u).

∂̄_I z̄^J = δ_IJ. The conjugate of dWirtingerCoord_coordProj, read off through dWirtingerAntiDir_star_comp rather than recomputed. Used to assemble the coordinate-difference rule dWirtingerAntiCoord_coordDiff (§C).