isToolOf

P24520
predicate

Indicates that one entity functions as an instrument or means used by another entity to perform tasks or achieve goals.

All labels observed (18)

Label Occurrences
toolFor 77
isToolOf canonical 7
instrumentOf 4

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: isToolOf
Generated description
Indicates that one entity functions as an instrument or means used by another entity to perform tasks or achieve goals.

Sample triples (115)

Subject Object
Borel–Weil theorem classification of irreducible representations of compact Lie groups via predicate surface "toolFor"
Borel–Weil theorem geometric representation theory via predicate surface "toolFor"
Leray–Schauder degree nonlinear operator equations via predicate surface "toolFor"
Leray–Schauder degree integral equations via predicate surface "toolFor"
Leray–Schauder degree nonlinear boundary value problems via predicate surface "toolFor"
de Rham cohomology classification of smooth manifolds up to homotopy type via predicate surface "toolFor"
de Rham cohomology study of integration of differential forms via predicate surface "toolFor"
de Rham cohomology formulation of Stokes theorem in cohomological terms via predicate surface "toolFor"
Hamiltonian optics deriving optical invariants via predicate surface "toolFor"
Hamiltonian optics analyzing stability of optical resonators via predicate surface "toolFor"
Hamiltonian optics designing aplanatic optical systems via predicate surface "toolFor"
Missy Armitage silver spoon via predicate surface "weaponOrTool"
Missy Armitage teacup via predicate surface "weaponOrTool"
Lasker–Noether theorem on primary decomposition analyzing structure of ideals via predicate surface "toolFor"
Lasker–Noether theorem on primary decomposition studying local properties of schemes via predicate surface "toolFor"
Lasker–Noether theorem on primary decomposition computing associated primes via predicate surface "toolFor"
Krull–Gabriel dimension analyzing composition series of objects in abelian categories via predicate surface "toolFor"
Krull–Gabriel dimension stratifying module categories by complexity via predicate surface "toolFor"
Yoneda lemma defining limits and colimits via representable functors via predicate surface "toolFor"
Yoneda lemma studying adjoint functors via predicate surface "toolFor"
Yoneda lemma categorical algebra via predicate surface "toolFor"
Yoneda lemma topos theory via predicate surface "toolFor"
Yoneda lemma homological algebra via predicate surface "toolFor"
Yoneda lemma algebraic geometry via functor of points via predicate surface "toolFor"
Morawetz inequalities analysis of obstacle scattering via predicate surface "toolFor"
Morawetz inequalities black hole spacetime wave analysis via predicate surface "toolFor"
Morawetz inequalities stability analysis of solutions via predicate surface "toolFor"
Combinatorial Nullstellensatz proving combinatorial identities via predicate surface "toolFor"
Combinatorial Nullstellensatz bounding sizes of combinatorial configurations via predicate surface "toolFor"
Combinatorial Nullstellensatz establishing existence of transversals via predicate surface "toolFor"
Combinatorial Nullstellensatz coloring problems in graphs and hypergraphs via predicate surface "toolFor"
Thom transversality theorem classification of singularities of smooth maps via predicate surface "toolFor"
Thom transversality theorem proofs of genericity of Morse functions via predicate surface "toolFor"
Thom transversality theorem intersection theory on manifolds via predicate surface "toolFor"
East German football league system state sports policy via predicate surface "wasToolFor"
Linton Heathcliff Heathcliff via predicate surface "usedAsToolBy" NERFINISHED
Question Hour legislative oversight of the executive
van der Corput method for estimating exponential sums proving equidistribution of polynomial sequences modulo 1 via predicate surface "toolFor"
van der Corput method for estimating exponential sums bounding error terms in asymptotic formulas via predicate surface "toolFor"
van der Corput method for estimating exponential sums estimating exponential integrals via discretization via predicate surface "toolFor"
crème brûlée kitchen blowtorch via predicate surface "requiresKitchenTool"
crème brûlée oven via predicate surface "requiresKitchenTool"
Zassenhaus filtration constructing associated graded Lie rings of groups via predicate surface "toolFor"
Zassenhaus filtration analyzing generators and relations in pro-p groups via predicate surface "toolFor"
Separatist Alliance Sith via predicate surface "usedAsToolBy" NERFINISHED
Separatist Alliance Darth Sidious via predicate surface "usedAsToolBy" NERFINISHED
Herbrand quotient relating arithmetic invariants to cohomology groups via predicate surface "toolFor"
Intha people single oar via predicate surface "rowingTool"
Cauchy–Pompeiu formula solving inhomogeneous Cauchy–Riemann equations via predicate surface "toolFor"
Cauchy–Pompeiu formula representation of non-holomorphic functions via predicate surface "toolFor"