holdsIn
P17841
predicate
Indicates that a relationship, condition, or event is valid or occurs within a specified time interval or temporal context.
All labels observed (2)
| Label | Occurrences |
|---|---|
| holdsIn canonical | 94 |
| Rostker v. GoldbergHolding | 1 |
Sample triples (95)
| Subject | Object |
|---|---|
| Cantor’s paradox | naive set theory ⓘ |
| Minkowski inequality | Lebesgue spaces ⓘ |
| Minkowski inequality | sequence spaces ℓ^p ⓘ |
| Minkowski inequality | finite-dimensional Euclidean spaces ⓘ |
| Glicksberg fixed-point theorem | Hausdorff locally convex topological vector spaces ⓘ |
|
Gauss’s law
surface form:
Gauss's law
|
vacuum ⓘ |
|
Gauss’s law
surface form:
Gauss's law
|
linear dielectric media ⓘ |
| Gauss's law for magnetism | vacuum ⓘ |
| Gauss's law for magnetism | linear media ⓘ |
| Gauss's law for magnetism | nonlinear media ⓘ |
| Hilbert’s Nullstellensatz | finitely generated polynomial algebras over algebraically closed fields ⓘ |
| Military Selective Service Act | male-only registration upheld as constitutional at that time via predicate surface "Rostker v. GoldbergHolding" ⓘ |
| Wick’s theorem |
Heisenberg operator formulation of quantum mechanics
ⓘ
surface form:
Heisenberg picture of quantum field theory
|
| Tarski's undefinability theorem | any consistent, sufficiently strong, effectively axiomatizable theory extending Robinson arithmetic ⓘ |
| Cantor’s theorem | Zermelo–Fraenkel set theory ⓘ |
| Cantor’s theorem |
ZF
ⓘ
surface form:
ZFC
|
| Cantor’s theorem | most standard axiomatic set theories ⓘ |
| identity of indiscernibles | many classical metaphysical systems ⓘ |
| Wigner–Eckart theorem | Hilbert space of angular momentum eigenstates ⓘ |
| Hume’s Principle (derivable, not postulated) |
Frege’s system in "Grundgesetze der Arithmetik"
ⓘ
surface form:
Frege’s logical system
|
| Weierstrass preparation theorem | ring of convergent power series in several complex variables ⓘ |
| Carathéodory’s theorem in convex geometry | any real finite-dimensional normed vector space (via linear isomorphism with ℝⁿ) ⓘ |
| Pythagorean theorem | Euclidean space ⓘ |
| Banach inverse mapping theorem | real Banach spaces ⓘ |
| Banach inverse mapping theorem | complex Banach spaces ⓘ |
| Fermat's theorem on sums of two squares | ring of Gaussian integers Z[i] ⓘ |
| Lagrange's theorem in group theory | finite abelian groups ⓘ |
| Lagrange's theorem in group theory | finite non-abelian groups ⓘ |
| Poincaré lemma | contractible smooth manifolds ⓘ |
| Poincaré lemma | star-shaped open subsets of R^n ⓘ |
| Cauchy integral theorem | complex plane ⓘ |
| Cauchy integral theorem | open subsets of the complex plane ⓘ |
| Cauchy integral formula | simply connected domains (with appropriate hypotheses) ⓘ |
| Schwarz lemma | unit disk in the complex plane ⓘ |
| Fourier inversion theorem |
Euclidean space
ⓘ
surface form:
Euclidean spaces Rn
|
| Euler’s theorem | multiplicative group of units modulo n ⓘ |
| Raychaudhuri equation |
Lorentzian geometry
ⓘ
surface form:
Lorentzian manifolds
|
| Raychaudhuri equation | Riemannian manifolds with appropriate interpretation ⓘ |
| Itô isometry | continuous-time stochastic processes ⓘ |
| Löb's theorem | Peano arithmetic ⓘ |
| Löb's theorem | many recursively axiomatizable extensions of Peano arithmetic ⓘ |
| Schmidt decomposition | finite-dimensional Hilbert spaces ⓘ |
| Banach–Steinhaus theorem | complete normed spaces ⓘ |
| Steinhaus theorem | Euclidean spaces R^n with Lebesgue measure ⓘ |
| Tychonoff theorem for products of compact spaces | product topology, not box topology ⓘ |
| Closed Graph Theorem | normed linear spaces that are complete ⓘ |
| De Morgan's laws | classical propositional logic ⓘ |
| De Morgan's laws | Boolean algebras NERFINISHED ⓘ |
| De Morgan's laws | set algebras ⓘ |
| fundamental theorem of arithmetic | ring of integers ⓘ |