Research proof index

Recursive enumerability of a predicate on a Primcodable type is equivalent to the recursive enumerability of the corresponding predicate on ℕ obtained by decoding.

Let $f$ be holomorphic on a punctured neighborhood of $p$. If $(s-p)f(s)\longrightarrow A\qquad(s\to p),$ then $f$ differs from its principal part $A/(s-p)$ by a bounded function on some punctured neighborhood of $p$. In asymptotic notation, $f(s)=\frac{A}{s-p}+O(1).$

Instantiating symbolic capabilities is associative. Substituting impl₁ into a profile c, and then substituting impl₂ into the resulting profile, is the same as substituting the composite implementation fun k ↦ (impl₁ k).instantiate impl₂ into c directly.

For any function F : ℍ → ℂ and t > 0, F.resToImagAxis (1/t) = F(S • (I*t)).

Real part of a product on the imaginary axis is the product of real parts, when both factors are real-valued there.

Restriction and slash action under S: $(F |_k S) (it) = (it)^{-k} * F(it)$