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.
Observed surface forms (8)
- usedToProve ×8
- isProvedBy ×2
- provenBy ×2
- theorem ×2
- originallyProvedBy ×1
- provedExistenceOf ×1
- proves ×1
- wasProvedPossibleBy ×1
Sample triples (21)
| Subject | Object |
|---|---|
| Ernst Zermelo |
axiom of choice
→
surface form:
well-ordering theorem
|
| Ferdinand von Lindemann | no straightedge-and-compass construction can square the circle → |
| Ferdinand von Lindemann | pi is transcendental → |
| Gauss map | Gauss–Bonnet theorem uses integral of Gaussian curvature derived from Gauss map via predicate surface "theorem" → |
| Gauss map | area of image under Gauss map relates to total curvature via predicate surface "theorem" → |
| Hilbert’s irreducibility theorem | David Hilbert via predicate surface "provenBy" → |
| Lax equivalence theorem | Peter Lax via predicate surface "provenBy" → |
| Noetherian induction | finiteness properties via predicate surface "usedToProve" → |
| Noetherian induction | structural properties of Noetherian rings via predicate surface "usedToProve" → |
| Noetherian induction | termination of algorithms via predicate surface "usedToProve" → |
| Riemann–Roch theorem | Bernhard Riemann via predicate surface "originallyProvedBy" → |
| Theorema Egregium |
Gaussian curvature
via predicate surface "proves"
→
surface form:
Gaussian curvature is invariant under local isometries of surfaces
|
| Tucker’s lemma | consensus halving theorems via predicate surface "usedToProve" → |
| Tucker’s lemma | necklace splitting theorems via predicate surface "usedToProve" → |
| Vitus Bering | strait between Asia and North America via predicate surface "provedExistenceOf" → |
| axiom schema of separation | existence of intersections of sets via predicate surface "usedToProve" → |
| axiom schema of separation | existence of many standard set-theoretic constructions via predicate surface "usedToProve" → |
| axiom schema of separation | existence of relative complements via predicate surface "usedToProve" → |
| construction of the regular 17-gon with straightedge and compass | Carl Friedrich Gauss via predicate surface "wasProvedPossibleBy" → |
| local existence and uniqueness theorem | Banach fixed-point theorem via predicate surface "isProvedBy" → |
| local existence and uniqueness theorem | Picard iteration via predicate surface "isProvedBy" → |