holdsIn

P17841

predicate

Indicates that a relationship, condition, or event is valid or occurs within a specified time interval or temporal context.

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All labels observed (2)

Label	Occurrences
holdsIn canonical	94
Rostker v. GoldbergHolding	1

Description generation (PDg)

The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.

Instruction

Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning.  
# Instructions
Focus on describing the relationship, not the entities themselves. 
# Response Format
Begin the description with \' Indicates...\'

Input

Predicate: holdsIn

Generated description

Indicates that a relationship, condition, or event is valid or occurs within a specified time interval or temporal context.

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 linked to: Gauss’s law	vacuum ⓘ
Gauss's law linked to: 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 picture of quantum field theory ⓘ linked to: Heisenberg operator formulation of quantum mechanics
Tarski's undefinability theorem	any consistent, sufficiently strong, effectively axiomatizable theory extending Robinson arithmetic ⓘ
Cantor’s theorem	Zermelo–Fraenkel set theory ⓘ
Cantor’s theorem	ZFC ⓘ linked to: ZF
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 logical system ⓘ linked to: Frege’s system in "Grundgesetze der Arithmetik"
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 spaces Rn ⓘ linked to: Euclidean space
Euler’s theorem	multiplicative group of units modulo n ⓘ
Raychaudhuri equation	Lorentzian manifolds ⓘ linked to: Lorentzian geometry
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 ⓘ linked to: Boolean algebra
De Morgan's laws	set algebras ⓘ
fundamental theorem of arithmetic	ring of integers ⓘ