holdsFor

P12018
predicate

Indicates that a particular relationship or condition remains true over a specified interval or duration of time.

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All labels observed (5)

Label Occurrences
holdsFor canonical 180
holdsOn 11
giltFür 8

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
Poincaré inequality bounded domains under mild regularity assumptions via predicate surface "holdsOn" ⓘ
Jordan–Hölder theorem finite solvable groups ⓘ
Jordan–Hölder theorem finite simple groups ⓘ
quadratic reciprocity law distinct odd primes p and q ⓘ
Hodge Conjecture divisors by Lefschetz (1,1)-theorem ⓘ
Birch and Swinnerton-Dyer Conjecture many elliptic curves in special cases ⓘ
Hasse principle quadratic forms over Q ⓘ
Hasse–Arf theorem finite abelian Galois extensions of non-archimedean local fields ⓘ
Cauchy interlacing theorem real eigenvalues ⓘ
Cauchy interlacing theorem ordered eigenvalues in nonincreasing order ⓘ
Hilbert’s fourteenth problem certain classes of groups and representations via predicate surface "trueFor" ⓘ
Hilbert’s fourteenth problem linearly reductive groups over fields of characteristic zero via predicate surface "trueFor" ⓘ
Hilbert’s fourteenth problem finite groups via predicate surface "trueFor" ⓘ
Hilbert’s fourteenth problem reductive algebraic groups acting linearly via predicate surface "trueFor" ⓘ
Hasse norm theorem cyclic Galois extensions ⓘ
Kirchenordnung der Evangelischen Landeskirche in Württemberg Evangelical Church of Württemberg via predicate surface "giltFür" ⓘ
surface form: Evangelische Landeskirche in Württemberg
Harish-Chandra isomorphism complex semisimple Lie algebra g with Cartan subalgebra h and Weyl group W ⓘ
Koebe quarter theorem complex-valued functions ⓘ
Dynkin formula diffusion processes ⓘ
Dynkin formula jump Markov processes ⓘ
Dynkin formula continuous-time Markov chains ⓘ
Grothendieck–Ogg–Shafarevich formula constructible ℓ-adic sheaves ⓘ
Grothendieck–Ogg–Shafarevich formula lisse ℓ-adic sheaves on open subsets of curves ⓘ
Milnor–Wood inequality flat PSL(2,R)-bundles over surfaces ⓘ
monotone convergence theorem σ-algebras ⓘ
monotone convergence theorem complete measures ⓘ
dominated convergence theorem complex-valued integrable functions ⓘ
dominated convergence theorem real-valued integrable functions ⓘ
Fatou's lemma extended real-valued functions ⓘ
Tonelli's theorem Lebesgue measure ⓘ
surface form: Lebesgue measure on Euclidean spaces
Tonelli's theorem general σ‑finite measure spaces ⓘ
Kolmogorov zero–one law countable sequences of independent random variables ⓘ
Hadamard inequality Hermitian positive semidefinite matrices via Gram representation ⓘ
Hadamard three-circle theorem entire functions ⓘ
Hadamard three-circle theorem holomorphic functions on annuli ⓘ
Itô isometry real-valued Brownian motion ⓘ
Itô isometry multi-dimensional Brownian motion ⓘ
Ramanujan–Petersson conjecture holomorphic cusp forms of any integral weight k ≥ 2 ⓘ
Jahn–Teller effect ground electronic states with degeneracy ⓘ
Jahn–Teller effect excited electronic states with degeneracy ⓘ
Young inequality for convolutions R^n with Lebesgue measure via predicate surface "holdsOn" ⓘ
Young inequality for convolutions locally compact abelian groups via predicate surface "holdsOn" ⓘ
Karamata's inequality strictly convex functions with strict inequality when sequences differ nontrivially ⓘ
Karamata's inequality strictly concave functions with strict reversed inequality when sequences differ nontrivially ⓘ
Kramers degeneracy nonrelativistic quantum systems with half-integer spin and time-reversal symmetry ⓘ
Kramers degeneracy relativistic fermions with time-reversal symmetry ⓘ
Banach–Stone theorem continuous real-valued functions on compact Hausdorff spaces ⓘ
Banach–Stone theorem continuous complex-valued functions on compact Hausdorff spaces ⓘ
Banach–Mazur theorem real separable Banach spaces ⓘ
Banach–Mazur theorem complex separable Banach spaces ⓘ