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
Ferdinand von Lindemann pi is transcendental ⓘ
Ferdinand von Lindemann no straightedge-and-compass construction can square the circle ⓘ
local existence and uniqueness theorem Picard iteration via predicate surface "isProvedBy" ⓘ
local existence and uniqueness theorem Banach fixed-point theorem via predicate surface "isProvedBy" ⓘ
Theorema Egregium Gaussian curvature via predicate surface "proves" ⓘ
surface form: Gaussian curvature is invariant under local isometries of surfaces
construction of the regular 17-gon with straightedge and compass Carl Friedrich Gauss via predicate surface "wasProvedPossibleBy" ⓘ
Noetherian induction termination of algorithms via predicate surface "usedToProve" ⓘ
Noetherian induction finiteness properties via predicate surface "usedToProve" ⓘ
Noetherian induction structural properties of Noetherian rings via predicate surface "usedToProve" ⓘ
Gauss map area of image under Gauss map relates to total curvature via predicate surface "theorem" ⓘ
Gauss map Gauss–Bonnet theorem uses integral of Gaussian curvature derived from Gauss map via predicate surface "theorem" ⓘ
Hilbert’s irreducibility theorem David Hilbert via predicate surface "provenBy" ⓘ
Ernst Zermelo axiom of choice ⓘ
surface form: well-ordering theorem
Riemann–Roch theorem Bernhard Riemann via predicate surface "originallyProvedBy" ⓘ
Tucker’s lemma necklace splitting theorems via predicate surface "usedToProve" ⓘ
Tucker’s lemma consensus halving theorems via predicate surface "usedToProve" ⓘ
Vitus Bering strait between Asia and North America via predicate surface "provedExistenceOf" ⓘ
Lax equivalence theorem Peter Lax via predicate surface "provenBy" ⓘ
axiom schema of separation existence of intersections of sets via predicate surface "usedToProve" ⓘ
axiom schema of separation existence of relative complements via predicate surface "usedToProve" ⓘ
axiom schema of separation existence of many standard set-theoretic constructions via predicate surface "usedToProve" ⓘ
Hardy–Littlewood maximal function almost everywhere convergence of averages via predicate surface "usedToProve" ⓘ
Hardy–Littlewood maximal function boundedness of Calderón–Zygmund operators via predicate surface "usedToProve" ⓘ
Paxos consensus algorithm Leslie Lamport via predicate surface "correctnessProvedBy" ⓘ
Lindemann
surface form: Ferdinand von Lindemann
π is a transcendental number ⓘ
Lindemann
surface form: Ferdinand von Lindemann
impossibility of squaring the circle with straightedge and compass ⓘ
Fermat's Last Theorem Richard Taylor via predicate surface "proofCompletedWith" ⓘ
Fermat's theorem on sums of two squares Joseph-Louis Lagrange via predicate surface "hasAlternativeProofBy" ⓘ
Fermat's theorem on sums of two squares Carl Friedrich Gauss via predicate surface "hasAlternativeProofBy" ⓘ
Halting problem Alan Turing via predicate surface "provenBy" ⓘ
Archimedean property of real numbers density of rational numbers in the real numbers via predicate surface "usedToProve" ⓘ
Archimedean property of real numbers existence of integer parts of real numbers via predicate surface "usedToProve" ⓘ
Archimedean property of real numbers existence of floor and ceiling functions on real numbers via predicate surface "usedToProve" ⓘ
Archimedean property of real numbers basic inequalities in analysis via predicate surface "usedToProve" ⓘ
Archimedean property of real numbers limit properties involving sequences 1/n via predicate surface "usedToProve" ⓘ
Archimedean property of real numbers that 1/n converges to 0 in the real numbers via predicate surface "usedToProve" ⓘ
On the Sphere and Cylinder volume of a sphere is two-thirds the volume of its circumscribed cylinder via predicate surface "proves" ⓘ
On the Sphere and Cylinder surface area of a sphere is equal to the lateral surface area of its circumscribed cylinder including bases via predicate surface "proves" ⓘ
On the Sphere and Cylinder surface area of a sphere is four times the area of its great circle via predicate surface "proves" ⓘ
On the Measurement of the Circle inequalities for pi via predicate surface "proves" ⓘ
On Floating Bodies conditions for a body to float or sink via predicate surface "proves" ⓘ
On the Equilibrium of Planes conditions for equilibrium of weights on a lever via predicate surface "proves" ⓘ
On the Equilibrium of Planes positions of centers of gravity of plane figures via predicate surface "proves" ⓘ
Quadrature of the Parabola area of parabolic segment equals 4/3 of reference triangle via predicate surface "proves" ⓘ
Cantor–Bernstein–Schröder theorem Felix Bernstein via predicate surface "originalProofBy" ⓘ
Michael Ventris Linear B ⓘ
surface form: Linear B represents an early form of Greek
Chebotarev density theorem Nikolai Chebotaryov via predicate surface "wasProvedBy" ⓘ
Cauchy convergence criterion convergence of numerical series via predicate surface "usedToProve" ⓘ
Cauchy convergence criterion existence of limits of sequences via predicate surface "usedToProve" ⓘ
Cauchy interlacing theorem eigenvalue bounds for Laplacian matrices of graphs via predicate surface "usedToProve" ⓘ