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.

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All labels observed (17)

Label Occurrences
usedToProve 60
proves 27
originallyProvedBy 17

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
Hausdorff maximal principle Tychonoff theorem (via equivalence with axiom of choice) via predicate surface "usedToProve" ⓘ
Gochang, Hwasun and Ganghwa Dolmen Sites development of prehistoric funerary practices in Korea via predicate surface "proves" ⓘ
Hurwitz quaternions Lagrange four-square theorem via predicate surface "usedToProve" ⓘ
Method of Exhaustion area of a circle equals pi times radius squared via predicate surface "usedToProve" ⓘ
Method of Exhaustion volume of a sphere equals four thirds pi times radius cubed via predicate surface "usedToProve" ⓘ
Method of Exhaustion volume of a cone equals one third base times height via predicate surface "usedToProve" ⓘ
Lefschetz duality properties of manifolds with nonempty boundary via predicate surface "usedToProve" ⓘ
Bernstein theorem antisymmetry of the injection-based preorder on cardinalities via predicate surface "proves" ⓘ
Bernstein theorem Felix Bernstein via predicate surface "originallyProvedBy" NERFINISHED ⓘ
Subspace theorem Wolfgang M. Schmidt via predicate surface "originallyProvedBy" NERFINISHED ⓘ
Mordell–Weil theorem Louis Mordell via predicate surface "originallyProvedBy" NERFINISHED ⓘ
Gauss sum quadratic reciprocity law via predicate surface "usedToProve" NERFINISHED ⓘ
Gauss sum properties of Dirichlet L-functions via predicate surface "usedToProve" ⓘ
Gauss sum non-vanishing of L-functions at certain points via predicate surface "usedToProve" ⓘ
Post correspondence problem undecidability of the halting problem variants via predicate surface "usedToProve" ⓘ
Post correspondence problem undecidability of problems in formal language theory via predicate surface "usedToProve" ⓘ
Post correspondence problem undecidability of context-free grammar equivalence via predicate surface "usedToProve" ⓘ
Post correspondence problem undecidability of Post normal system properties via predicate surface "usedToProve" ⓘ
Hopf invariant nontriviality of certain homotopy groups of spheres via predicate surface "usedToProve" ⓘ
"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds"
surface form: Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
finite-time extinction for Ricci flow on certain three-manifolds via predicate surface "proves" ⓘ
Book XII of Euclid's Elements areas of circles are proportional to squares of their diameters via predicate surface "proves" ⓘ
Book XII of Euclid's Elements volumes of cones and cylinders are proportional to bases and heights via predicate surface "proves" ⓘ
Book XII of Euclid's Elements volume of a cone is one third the volume of a cylinder on the same base and height via predicate surface "proves" ⓘ
Book XII of Euclid's Elements volume of a pyramid is one third the volume of a prism on the same base and height via predicate surface "proves" ⓘ
Book XII of Euclid's Elements volume relationships of spheres and cylinders via predicate surface "proves" ⓘ
Linnik’s theorem on the least prime in an arithmetic progression Yuri Linnik via predicate surface "originallyProvedBy" NERFINISHED ⓘ
zk-SNARKs knowledge of a witness for an NP statement via predicate surface "usedToProve" ⓘ
BEST theorem Nicolaas Govert de Bruijn via predicate surface "originallyProvedBy" NERFINISHED ⓘ
BEST theorem Tatyana van Aardenne-Ehrenfest via predicate surface "originallyProvedBy" NERFINISHED ⓘ
BEST theorem Cedric A. B. Smith via predicate surface "originallyProvedBy" NERFINISHED ⓘ
BEST theorem William T. Tutte via predicate surface "originallyProvedBy" NERFINISHED ⓘ
Cauchy net existence of limits in complete spaces via predicate surface "usedToProve" ⓘ
Cauchy–Binet formula properties of rank of matrix products via predicate surface "usedToProve" ⓘ
Cauchy–Binet formula inequalities for determinants via predicate surface "usedToProve" ⓘ
Cauchy–Binet formula Hadamard’s inequality in some settings via predicate surface "usedToProve" NERFINISHED ⓘ
Weyl inequalities stability results for eigenvalues via predicate surface "usedToProve" ⓘ
Weyl inequalities bounds for condition numbers of eigenvalues via predicate surface "usedToProve" ⓘ
Weyl inequalities spectral inclusion results via predicate surface "usedToProve" ⓘ
Yuri Matiyasevich that every recursively enumerable set is Diophantine ⓘ
Yuri Matiyasevich that there is no algorithm to decide solvability of arbitrary Diophantine equations in integers ⓘ
Kesten’s theorem Harry Kesten via predicate surface "provenBy" NERFINISHED ⓘ
Gentzen
surface form: Gerhard Gentzen
cut-elimination theorem for sequent calculus ⓘ
Gentzen
surface form: Gerhard Gentzen
consistency of first-order Peano arithmetic ⓘ
proof of the Milnor conjecture Milnor conjecture via predicate surface "proves" NERFINISHED ⓘ
proof of the Milnor conjecture fields of characteristic not equal to 2 via predicate surface "provesFor" ⓘ
Seiberg–Witten invariants Thom conjecture for CP^2 via predicate surface "usedToProve" NERFINISHED ⓘ
Seiberg–Witten invariants constraints on intersection forms of 4-manifolds via predicate surface "usedToProve" ⓘ
Siegel mass formula Carl Ludwig Siegel via predicate surface "provenBy" NERFINISHED ⓘ
Cartan–Eilenberg spectral sequence relations between Ext and Tor of composite functors via predicate surface "usedToProve" ⓘ
Mostow rigidity theorem George Daniel Mostow via predicate surface "provenBy" NERFINISHED ⓘ