proved
P21917
predicate
Indicates that one entity has demonstrated the truth or validity of another entity (such as a statement, theorem, or claim) through logical or evidential means.
All labels observed (17)
| Label | Occurrences |
|---|---|
| usedToProve | 60 |
| proves | 27 |
| originallyProvedBy | 17 |
| provenBy | 13 |
| proved canonical | 12 |
| provesProperty | 5 |
| theorem | 3 |
| elementaryProofBy | 2 |
| hasAlternativeProofBy | 2 |
| isProvedBy | 2 |
| wasProvedBy | 2 |
| correctnessProvedBy | 1 |
| originalProofBy | 1 |
| proofCompletedWith | 1 |
| provedExistenceOf | 1 |
| provesFor | 1 |
| wasProvedPossibleBy | 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: proved
Generated description
Indicates that one entity has demonstrated the truth or validity of another entity (such as a statement, theorem, or claim) through logical or evidential means.
Sample triples (151)
| Subject | Object |
|---|---|
| Cauchy interlacing theorem | interlacing families of polynomials in combinatorics via predicate surface "usedToProve" ⓘ |
| Hasse norm theorem | Helmut Hasse via predicate surface "provenBy" ⓘ |
| Gerhard Gentzen | consistency of Peano arithmetic relative to transfinite induction up to ε₀ ⓘ |
| Grothendieck spectral sequence | relations between different cohomology theories via predicate surface "usedToProve" ⓘ |
| Serre spectral sequence | Serre’s finiteness theorem for homotopy groups of spheres (via related methods) via predicate surface "usedToProve" ⓘ |
| prime number theorem | Atle Selberg via predicate surface "elementaryProofBy" ⓘ |
| prime number theorem |
Pál Erdős
via predicate surface "elementaryProofBy"
ⓘ
surface form:
Paul Erdős
|
| Dehn lemma | Max Dehn via predicate surface "originallyProvedBy" ⓘ |
| monotone convergence theorem |
dominated convergence theorem
via predicate surface "usedToProve"
ⓘ
surface form:
Lebesgue dominated convergence theorem
|
| monotone convergence theorem |
Fubini's theorem
via predicate surface "usedToProve"
ⓘ
surface form:
Fubini theorem (components of proofs)
|
| monotone convergence theorem |
Tonelli's theorem
via predicate surface "usedToProve"
ⓘ
surface form:
Tonelli theorem
|
|
Chebyshev functions
surface form:
Chebyshev function ψ(x)
|
prime number theorem via predicate surface "usedToProve" ⓘ |
| Ramanujan–Nagell equation | Trygve Nagell via predicate surface "wasProvedBy" ⓘ |
|
Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"
surface form:
The Consistency of the Continuum Hypothesis
|
L satisfies all axioms of Zermelo–Fraenkel set theory via predicate surface "provesProperty" ⓘ |
|
Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"
surface form:
The Consistency of the Continuum Hypothesis
|
L satisfies the Axiom of Choice via predicate surface "provesProperty" ⓘ |
|
Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"
surface form:
The Consistency of the Continuum Hypothesis
|
L satisfies the Generalized Continuum Hypothesis via predicate surface "provesProperty" ⓘ |
|
Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"
surface form:
The Consistency of the Continuum Hypothesis
|
L is a transitive class via predicate surface "provesProperty" ⓘ |
|
Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"
surface form:
The Consistency of the Continuum Hypothesis
|
every set in L is constructible from earlier stages of the hierarchy via predicate surface "provesProperty" ⓘ |
|
Axiom of Extensionality in set theory
surface form:
Axiom of Extensionality
|
uniqueness of the empty set via predicate surface "usedToProve" ⓘ |
|
Axiom of Extensionality in set theory
surface form:
Axiom of Extensionality
|
uniqueness of set-theoretic constructions defined by comprehension-like conditions via predicate surface "usedToProve" ⓘ |
| Runge approximation theorem | Carl Runge via predicate surface "provenBy" NERFINISHED ⓘ |
| Cartan theorems A and B | Henri Cartan via predicate surface "provenBy" NERFINISHED ⓘ |
| Almost Periodic Functions | existence of mean values for almost periodic functions via predicate surface "proves" ⓘ |
| Almost Periodic Functions | uniqueness of Bohr–Fourier series for almost periodic functions via predicate surface "proves" ⓘ |
| Almost Periodic Functions | closure of almost periodic functions under uniform limits via predicate surface "proves" ⓘ |
| Almost Periodic Functions | closure of almost periodic functions under translations via predicate surface "proves" ⓘ |
| Almost Periodic Functions | closure of almost periodic functions under addition and multiplication via predicate surface "proves" ⓘ |
| Almost Periodic Functions | Bohr's fundamental theorem on almost periodic functions via predicate surface "proves" ⓘ |
| Helly’s theorem | Eduard Helly via predicate surface "originallyProvedBy" NERFINISHED ⓘ |
| Cook–Levin theorem | Stephen Cook via predicate surface "originallyProvedBy" NERFINISHED ⓘ |
| Cook–Levin theorem | NP-completeness of other problems via reductions from SAT via predicate surface "usedToProve" ⓘ |
| Chen Jingrun | Chen’s theorem on Goldbach’s conjecture NERFINISHED ⓘ |
| Faltings' theorem | Mordell conjecture via predicate surface "proves" NERFINISHED ⓘ |
| Lempert function on convex domains | equivalence of Kobayashi and Carathéodory distances on certain convex domains via predicate surface "usedToProve" ⓘ |
| Carmichael number | Alford–Granville–Pomerance proved in 1994 that there are infinitely many Carmichael numbers via predicate surface "theorem" NERFINISHED ⓘ |
| Erdős–Ko–Rado theorem | Paul Erdős via predicate surface "originallyProvedBy" NERFINISHED ⓘ |
| Erdős–Ko–Rado theorem | Chao Ko via predicate surface "originallyProvedBy" NERFINISHED ⓘ |
| Erdős–Ko–Rado theorem | Richard Rado via predicate surface "originallyProvedBy" NERFINISHED ⓘ |
| Chevalley–Warning theorem | Claude Chevalley via predicate surface "originallyProvedBy" NERFINISHED ⓘ |
| Chevalley–Warning theorem | Ernst Warning via predicate surface "originallyProvedBy" NERFINISHED ⓘ |
| Bombieri–Vinogradov theorem | Enrico Bombieri via predicate surface "provenBy" NERFINISHED ⓘ |
| Bombieri–Vinogradov theorem | A. I. Vinogradov via predicate surface "provenBy" NERFINISHED ⓘ |
| Undirected connectivity in log-space | existence of a deterministic log-space algorithm for undirected s-t connectivity via predicate surface "proves" ⓘ |
| Undirected connectivity in log-space | every undirected graph connectivity instance can be solved in O(log n) space deterministically via predicate surface "proves" ⓘ |
| LLN | Chebyshev via predicate surface "provenBy" NERFINISHED ⓘ |
| LLN | Kolmogorov via predicate surface "provenBy" NERFINISHED ⓘ |
| Leibniz rule | properties of polynomial derivatives via predicate surface "usedToProve" ⓘ |
| Leibniz rule | Leibniz formula for higher derivatives of products via predicate surface "usedToProve" NERFINISHED ⓘ |
| Hausdorff maximal principle | existence of bases in vector spaces via predicate surface "usedToProve" ⓘ |
| Hausdorff maximal principle | existence of maximal ideals in rings via predicate surface "usedToProve" ⓘ |