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 |
|---|---|
| Kakutani fixed-point theorem | topological arguments ⓘ |
| Kakutani fixed-point theorem | use of Brouwer fixed-point theorem ⓘ |
| binomial theorem | mathematical induction via predicate surface "canBeProvedBy" ⓘ |
| binomial theorem | combinatorial arguments via predicate surface "canBeProvedBy" ⓘ |
| binomial theorem | Pascal's identity via predicate surface "canBeProvedBy" ⓘ |
| Cantor’s paradox | diagonalization ⓘ |
| Cantor’s paradox | cardinality comparison ⓘ |
| Brouwer fixed-point theorem | topological methods via predicate surface "proofMethod" ⓘ |
| Brouwer fixed-point theorem | homology theory via predicate surface "proofMethod" ⓘ |
| Brouwer fixed-point theorem | degree theory via predicate surface "proofMethod" ⓘ |
| Brouwer fixed-point theorem | combinatorial arguments via predicate surface "proofMethod" ⓘ |
| multinomial theorem | induction on n via predicate surface "proofMethods" ⓘ |
| multinomial theorem | combinatorial argument via predicate surface "proofMethods" ⓘ |
| multinomial theorem | generating functions via predicate surface "proofMethods" ⓘ |
| Pascal's identity | combinatorial argument ⓘ |
| Pascal's identity | algebraic manipulation of binomial coefficients ⓘ |
| Pascal's identity | generating functions ⓘ |
| Hilbert basis theorem | induction on the number of variables via predicate surface "proofTechnique" ⓘ |
| Hilbert basis theorem | use of leading coefficients and degrees of polynomials via predicate surface "proofTechnique" ⓘ |
| Ralph Plaisted expedition | aircraft position check at the Pole via predicate surface "hasVerificationType" ⓘ |
| Riemann mapping theorem | normal families via predicate surface "proofMethod" ⓘ |
| Riemann mapping theorem | Montel theorem via predicate surface "proofMethod" ⓘ |
| Riemann mapping theorem | extremal problems for holomorphic functions via predicate surface "proofMethod" ⓘ |
| Riemann mapping theorem | Dirichlet principle (historically) via predicate surface "proofMethod" ⓘ |
| Tucker’s lemma | topological methods ⓘ |
| Tucker’s lemma | combinatorial methods ⓘ |
| PCP theorem | non-adaptive probabilistically checkable proofs via predicate surface "proofType" ⓘ |
| PCP theorem | adaptive probabilistically checkable proofs via predicate surface "proofType" ⓘ |
| completeness theorem for first-order logic | reduction to Skolem normal form and construction of a countable model via predicate surface "originalProofMethod" ⓘ |
| completeness theorem for first-order logic | Henkin construction via predicate surface "laterProofMethod" ⓘ |
| completeness theorem for first-order logic | canonical model construction via predicate surface "laterProofMethod" ⓘ |
| completeness theorem for first-order logic | tableau methods via predicate surface "laterProofMethod" ⓘ |
| completeness theorem for first-order logic | sequent calculus proofs via predicate surface "laterProofMethod" ⓘ |
| Weierstrass approximation theorem | trigonometric polynomials and substitution via predicate surface "originalProofMethod" ⓘ |
| Weierstrass approximation theorem | Bernstein polynomials via predicate surface "alternativeProofMethod" ⓘ |
| Weierstrass approximation theorem | convolution with approximate identities via predicate surface "alternativeProofMethod" ⓘ |
| Carathéodory’s theorem in convex geometry | induction on the dimension n via predicate surface "proofTechnique" ⓘ |
| Carathéodory’s theorem in convex geometry | use of affine dependence and Radon partitions via predicate surface "proofTechnique" ⓘ |
| Sperner's lemma | parity argument ⓘ |
| Sperner's lemma | induction on dimension ⓘ |
| Pythagorean theorem | geometric proofs via predicate surface "proofType" ⓘ |
| Pythagorean theorem | algebraic proofs via predicate surface "proofType" ⓘ |
| Pythagorean theorem | dissection proofs via predicate surface "proofType" ⓘ |
| Pythagorean theorem | similarity-based proofs via predicate surface "proofType" ⓘ |
| Banach inverse mapping theorem | Baire category theorem via predicate surface "proofTechnique" ⓘ |
| Banach inverse mapping theorem | Neumann series for operators via predicate surface "proofTechnique" ⓘ |
| Fermat's little theorem | group theory via predicate surface "proofTechnique" ⓘ |
| Fermat's little theorem | combinatorial arguments via predicate surface "proofTechnique" ⓘ |
| Fermat's little theorem | induction on exponents via predicate surface "proofTechnique" ⓘ |
| Fermat's theorem on sums of two squares | infinite descent via predicate surface "proofTechnique" ⓘ |