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 |
|---|---|
| Robertson–Schrödinger uncertainty relation | any pair of self-adjoint operators with finite variances ⓘ |
| Hardy inequality | 1-dimensional domains ⓘ |
| Hardy inequality | n-dimensional Euclidean space ⓘ |
| Hardy inequality | radial functions in R^n ⓘ |
|
Neumann’s principle in crystallography
surface form:
Neumann’s principle
|
all 32 crystallographic point groups ⓘ |
| Kummer congruences | even indices of Bernoulli numbers ⓘ |
| Hamming bound | linear codes ⓘ |
| Hamming bound | nonlinear codes ⓘ |
| Hahn decomposition theorem | finite signed measures ⓘ |
| Hahn decomposition theorem | σ-finite signed measures ⓘ |
| Hahn decomposition theorem | general signed measures on measurable spaces ⓘ |
| Helly’s theorem | finite families of convex sets ⓘ |
| Radon’s theorem | real affine spaces ⓘ |
| Weyl dimension formula | simple Lie algebras ⓘ |
| Weyl dimension formula | reductive Lie algebras with finite center ⓘ |
| Gibbs–Duhem equation | closed systems with variable composition ⓘ |
| Pythagorean identity in trigonometry | all real angles θ ⓘ |
| Pythagorean identity in trigonometry | all complex angles θ ⓘ |
| Pythagorean identity in trigonometry | θ = 0 via predicate surface "trueFor" ⓘ |
| Pythagorean identity in trigonometry | θ = π/2 via predicate surface "trueFor" ⓘ |
| Pythagorean identity in trigonometry | θ = π via predicate surface "trueFor" ⓘ |
| Pythagorean identity in trigonometry | θ = 2π via predicate surface "trueFor" ⓘ |
| open mapping theorem | complex Banach spaces ⓘ |
| open mapping theorem | real Banach spaces ⓘ |
| Wilson's theorem | every prime number p ⓘ |
| Hard Lefschetz theorem | smooth projective varieties over the complex numbers ⓘ |
| Drucker stability postulate in plasticity | incremental stress–strain processes ⓘ |
| Coleman theorem on symmetry breaking in two dimensions | continuous internal symmetries ⓘ |
| Coleman theorem on symmetry breaking in two dimensions | global symmetries ⓘ |
| Leibniz rule | real-valued differentiable functions ⓘ |
| Leibniz rule | complex-valued differentiable functions ⓘ |
| Leibniz rule | differentiable vector-valued functions ⓘ |
| Leibniz rule | differential operators ⓘ |
| Cartan formula | all degrees of differential forms ⓘ |
| Cartan formula | smooth vector fields ⓘ |
| Cartan magic formula | any smooth vector field X ⓘ |
| Cartan magic formula | any smooth differential form ω ⓘ |
| Lenzsche Regel | elektromagnetische Induktion via predicate surface "giltFür" ⓘ |
| Lenzsche Regel | induzierte Ströme in Leiterschleifen via predicate surface "giltFür" ⓘ |
| Lenzsche Regel | induzierte Spannungen in elektrischen Schaltkreisen via predicate surface "giltFür" ⓘ |
| Bochner–Kodaira–Nakano identity | compact Kähler manifolds via predicate surface "holdsOn" ⓘ |
| Bochner–Kodaira–Nakano identity | non-compact complete Kähler manifolds (with suitable conditions) via predicate surface "holdsOn" ⓘ |
| Cauchy's theorem in group theory | finite abelian groups ⓘ |
| Cauchy's theorem in group theory | finite non-abelian groups ⓘ |
| orbit-stabilizer theorem | left group actions ⓘ |
| orbit-stabilizer theorem | right group actions ⓘ |
| orbit-stabilizer theorem | actions by permutations ⓘ |
| orbit-stabilizer theorem | actions by conjugation ⓘ |
| Liouville's theorem in Hamiltonian mechanics | closed Hamiltonian systems ⓘ |
| Alexander duality | finite CW-complexes embedded in spheres ⓘ |