hasProofMethod
P7024
predicate
Indicates that there exists a specific method or technique used to establish or demonstrate the validity of something (such as a statement, claim, or theorem).
All labels observed (19)
| Label | Occurrences |
|---|---|
| proofTechnique | 48 |
| hasProofMethod canonical | 38 |
| hasProofTechnique | 28 |
| proofMethod | 28 |
| canBeProvedBy | 7 |
| methodOfProof | 7 |
| proofMethods | 7 |
| proofType | 6 |
| proofMethodsInclude | 5 |
| laterProofMethod | 4 |
| alternativeProofMethod | 3 |
| hasMethodOfIdentification | 3 |
| isProvedUsing | 3 |
| originalProofMethod | 3 |
| hasProofSystem | 2 |
| VoisinProofMethod | 1 |
| hasProofType | 1 |
| hasStandardProofMethod | 1 |
| hasVerificationType | 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: hasProofMethod
Generated description
Indicates that there exists a specific method or technique used to establish or demonstrate the validity of something (such as a statement, claim, or theorem).
Sample triples (196)
| Subject | Object |
|---|---|
| Cayley–Hamilton theorem | determinant-based arguments via predicate surface "proofMethods" ⓘ |
| Cayley–Hamilton theorem | module-theoretic arguments via predicate surface "proofMethods" ⓘ |
| Cayley–Hamilton theorem | Jordan canonical form via predicate surface "proofMethods" NERFINISHED ⓘ |
| Combinatorial Nullstellensatz | induction on degree via predicate surface "hasProofTechnique" ⓘ |
| Combinatorial Nullstellensatz | Lagrange interpolation via predicate surface "hasProofTechnique" NERFINISHED ⓘ |
| Combinatorial Nullstellensatz | algebraic manipulation of coefficients via predicate surface "hasProofTechnique" ⓘ |
| Bernstein theorem | construction of a bijection from two injections ⓘ |
| Bernstein theorem | set-theoretic decomposition of domains ⓘ |
| Eilenberg–Zilber theorem | explicit combinatorial chain maps via predicate surface "hasProofTechnique" ⓘ |
| Eilenberg–Zilber theorem | acyclic models via predicate surface "hasProofTechnique" ⓘ |
| Hurwitz theorem | continued fraction expansion of irrationals ⓘ |
| Hurwitz theorem | properties of convergents ⓘ |
| quartic reciprocity law | Gauss sums via predicate surface "proofTechnique" NERFINISHED ⓘ |
| quartic reciprocity law | algebraic number theory methods via predicate surface "proofTechnique" ⓘ |
| quartic reciprocity law | ideal-theoretic methods via predicate surface "proofTechnique" ⓘ |
| Euler pentagonal number theorem | generating functions via predicate surface "hasProofTechnique" ⓘ |
| Euler pentagonal number theorem | combinatorial arguments via predicate surface "hasProofTechnique" ⓘ |
| Euler pentagonal number theorem | manipulation of infinite products via predicate surface "hasProofTechnique" ⓘ |
|
Menger theorem in graph theory
surface form:
Menger's theorem (graph theory)
|
reduction to max-flow min-cut (modern proofs) ⓘ |
|
Menger theorem in graph theory
surface form:
Menger's theorem (graph theory)
|
combinatorial arguments ⓘ |
| Graham–Pollak theorem | linear algebra ⓘ |
| Graham–Pollak theorem | matrix rank arguments ⓘ |
| Graham–Pollak theorem | incidence matrix techniques ⓘ |
| Turán's theorem | averaging arguments via predicate surface "proofMethod" ⓘ |
| Turán's theorem | symmetrization via predicate surface "proofMethod" ⓘ |
| Turán's theorem | induction on the number of vertices via predicate surface "proofMethod" ⓘ |
| Siegel's theorem on integral points | Diophantine approximation methods via predicate surface "proofTechnique" ⓘ |
| Siegel's theorem on integral points | Thue–Siegel method via predicate surface "proofTechnique" NERFINISHED ⓘ |
| Cauchy’s mean value theorem | application of Rolle’s theorem to an auxiliary function via predicate surface "proofMethod" ⓘ |
| Morera's theorem | approximation of curves by polygonal paths or triangles via predicate surface "proofTechnique" ⓘ |
| Davis–Putnam–Robinson–Matiyasevich theorem | encoding of recursively enumerable sets by Diophantine equations via predicate surface "proofTechnique" ⓘ |
| Davis–Putnam–Robinson–Matiyasevich theorem | use of Fibonacci numbers in Matiyasevich's final step via predicate surface "proofTechnique" ⓘ |
|
Liouville's theorem
surface form:
Liouville's theorem (complex analysis)
|
Cauchy integral formula via predicate surface "proofMethod" NERFINISHED ⓘ |
|
Liouville's theorem
surface form:
Liouville's theorem (complex analysis)
|
Cauchy estimates via predicate surface "proofMethod" NERFINISHED ⓘ |
|
Liouville's theorem
surface form:
Liouville's theorem (complex analysis)
|
maximum modulus principle via predicate surface "proofMethod" ⓘ |
| Lax–Milgram theorem | functional analytic methods via predicate surface "hasProofTechnique" ⓘ |
| Lax–Milgram theorem | use of Riesz isomorphism between Hilbert space and its dual via predicate surface "hasProofTechnique" ⓘ |
| Robbins theorem | graph-theoretic arguments via predicate surface "proofTechnique" ⓘ |
| Shibboleth incident | pronunciation test via predicate surface "hasMethodOfIdentification" ⓘ |
| Malgrange–Ehrenpreis theorem | Fourier analytic methods via predicate surface "proofTechnique" ⓘ |
| Malgrange–Ehrenpreis theorem | complex analysis in several variables via predicate surface "proofTechnique" ⓘ |
| Bieberbach conjecture | Loewner chain method via predicate surface "methodOfProof" NERFINISHED ⓘ |
| Bieberbach conjecture | Hilbert space of entire functions via predicate surface "methodOfProof" ⓘ |
| Green’s conjecture | use of K3 surfaces and their hyperplane sections via predicate surface "VoisinProofMethod" ⓘ |
| Maschke’s theorem | averaging over the group via predicate surface "hasProofTechnique" ⓘ |
| Maschke’s theorem | construction of invariant complements via predicate surface "hasProofTechnique" ⓘ |