holdsFor
P12018
predicate
Indicates that a particular relationship or condition remains true over a specified interval or duration of time.
All labels observed (5)
| Label | Occurrences |
|---|---|
| holdsFor canonical | 180 |
| holdsOn | 11 |
| giltFür | 8 |
| trueFor | 8 |
| hedgingHorizon | 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: holdsFor
Generated description
Indicates that a particular relationship or condition remains true over a specified interval or duration of time.
Sample triples (208)
| Subject | Object |
|---|---|
| Alexander duality | polyhedra embedded in spheres ⓘ |
| Korn inequality | sufficiently regular domains via predicate surface "holdsOn" ⓘ |
| rank–nullity theorem | finite-dimensional vector spaces ⓘ |
| Alon–Boppana bound | families of finite d-regular graphs with growing number of vertices ⓘ |
| Lefschetz duality | coefficients in a field ⓘ |
| Lefschetz duality | coefficients in a principal ideal domain ⓘ |
| Eilenberg–Zilber theorem | pairs of topological spaces X and Y ⓘ |
| Dirichlet approximation theorem | every real number ⓘ |
| Dirichlet approximation theorem | every positive integer N ⓘ |
| Gauss–Codazzi equations | hypersurfaces ⓘ |
| Gauss–Codazzi equations | submanifolds of arbitrary codimension ⓘ |
| Brillouin theorem | restricted Hartree–Fock NERFINISHED ⓘ |
| Brillouin theorem | unrestricted Hartree–Fock ⓘ |
| Gemeindeordnung Baden-Württemberg | Gemeinden in Baden-Württemberg via predicate surface "giltFür" ⓘ |
| Jacobi's theorem on determinants | complex matrices ⓘ |
| Jacobi's theorem on determinants | real matrices ⓘ |
| Jacobi's theorem on determinants | matrices over a commutative field ⓘ |
| Riesz rearrangement inequality | Lebesgue measurable functions ⓘ |
| correspondence principle | average behavior of quantum systems ⓘ |
| BEST theorem | finite directed graphs ⓘ |
| Koksma–Hlawka inequality | any dimension s ≥ 1 ⓘ |
| Cauchy’s integral test | series with terms f(n)=1/n^p where p>0 ⓘ |
| Bolzano–Weierstrass theorem | closed and bounded subsets of ℝⁿ ⓘ |
| Cauchy–Binet formula | matrices over a commutative ring ⓘ |
| Cauchy–Binet formula | matrices over a field ⓘ |
| Weyl inequalities | complex Hermitian matrices ⓘ |
| Weyl inequalities | real symmetric matrices ⓘ |
| Cauchy completeness | real numbers with the usual metric ⓘ |
| Cauchy completeness | complex numbers with the usual metric ⓘ |
| Zassenhaus conjecture | finite nilpotent groups ⓘ |
| Zassenhaus conjecture | finite cyclic groups ⓘ |
| Zassenhaus conjecture | finite abelian groups ⓘ |
| Zassenhaus conjecture | many classes of solvable groups ⓘ |
| zeroth law of black hole mechanics | axisymmetric stationary black holes ⓘ |
| zeroth law of black hole mechanics | asymptotically flat stationary black holes ⓘ |
| Grundsätze der kirchlichen Disziplinarordnung | kirchliche Amtsträger via predicate surface "giltFür" ⓘ |
| Grundsätze der kirchlichen Disziplinarordnung | Pfarrerinnen und Pfarrer der Evangelischen Landeskirche in Württemberg via predicate surface "giltFür" ⓘ |
| Grundsätze der kirchlichen Disziplinarordnung | kirchliche Beamte via predicate surface "giltFür" ⓘ |
| Harish-Chandra regularity theorem | connected real reductive Lie groups ⓘ |
| Harish-Chandra regularity theorem | finite-length admissible representations ⓘ |
| Plancherel theorem for locally compact abelian groups | second countable locally compact abelian groups ⓘ |
| Dini's theorem | real-valued functions ⓘ |
| Dini's theorem | complex-valued functions ⓘ |
| Dini's theorem | continuous functions on compact Hausdorff spaces ⓘ |
| Serre vanishing theorem | ample line bundle on a projective scheme ⓘ |
| Serre vanishing theorem | twists of coherent sheaves by high powers of an ample line bundle ⓘ |
| Slater’s condition | convex problems with nonempty interior of feasible set ⓘ |
| Wigner semicircle law | Gaussian Orthogonal Ensemble NERFINISHED ⓘ |
| Wigner semicircle law | Gaussian Unitary Ensemble NERFINISHED ⓘ |
| Wigner semicircle law | Gaussian Symplectic Ensemble NERFINISHED ⓘ |