holdsOver
P27214
predicate
Indicates that a certain condition, state, or relationship remains valid or continues to apply across a specified period, context, or range.
All labels observed (1)
| Label | Occurrences |
|---|---|
| holdsOver canonical | 18 |
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: holdsOver
Generated description
Indicates that a certain condition, state, or relationship remains valid or continues to apply across a specified period, context, or range.
Sample triples (18)
| Subject | Object |
|---|---|
| Noether normalization lemma | any field ⓘ |
| Hilbert’s irreducibility theorem | the rational numbers ⓘ |
| Hilbert’s irreducibility theorem | number fields ⓘ |
| Cauchy–Hadamard theorem | complex numbers ⓘ |
| Cauchy–Hadamard theorem | complete valued fields with absolute value ⓘ |
| Hurwitz bound on automorphism groups of curves | complex numbers ⓘ |
| Fitting lemma | Artinian modules ⓘ |
| Fitting lemma | Noetherian modules under suitable hypotheses ⓘ |
| Hermite–Minkowski theorem | the rational number field ℚ ⓘ |
| Sylvester’s law of inertia | the field of real numbers ⓘ |
| rank–nullity theorem | any field ⓘ |
| Cayley–Hamilton theorem | any commutative ring ⓘ |
| Cayley–Hamilton theorem | fields ⓘ |
| Mordell–Weil theorem | number fields ⓘ |
| Serre vanishing theorem | Noetherian base ring ⓘ |
| Maschke’s theorem | fields of characteristic zero ⓘ |
| Maschke’s theorem | fields of characteristic p not dividing the group order ⓘ |
| Schur’s lemma | any field for the first part ⓘ |