nothing to prove
Definition
A graph class is monadically dependent (also called monadically NIP) if it does not transduce the class of all graphs.
Lean source view on GitHub
| 1 | import Lax5.GraphClasses |
| 2 | import Lax5.GraphTransductions |
| 3 | |
| 4 | /-! |
| 5 | --- |
| 6 | title: Monadic dependence |
| 7 | type: definition |
| 8 | --- |
| 9 | A graph class is monadically dependent (also called monadically NIP) if |
| 10 | it does not transduce the class of all graphs. |
| 11 | |
| 12 | # Formalization notes |
| 13 | |
| 14 | This is the standard transduction-based definition from the model theory |
| 15 | of graph classes, stated over the transduction relation of the |
| 16 | prerequisite concepts. |
| 17 | -/ |
| 18 | |
| 19 | namespace Lax5.MonadicDependence |
| 20 | |
| 21 | open Lax5.GraphClasses |
| 22 | |
| 23 | /-- A graph class is monadically dependent if it does not transduce the |
| 24 | class of all finite simple graphs. -/ |
| 25 | def MonadicallyDependent (C : GraphClass) : Prop := |
| 26 | ¬ GraphTransductions.Transduces C allGraphs |
| 27 | |
| 28 | end Lax5.MonadicDependence |
| 29 |
Formalization notes
This is the standard transduction-based definition from the model theory of graph classes, stated over the transduction relation of the prerequisite concepts.
Mathlib imports
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