Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.simpleGraphOfStructure

(V : Type u) →
  [inst : FirstOrder.Language.graph.Structure V] → [V ⊨ FirstOrder.Language.Theory.simpleGraph] → SimpleGraph V

Any model of the theory of simple graphs represents a simple graph.

Defined in
Mathlib.ModelTheory.Graph
Cited by
3 results in Mathlib
Foundations
Depth 40 from the axioms · uses propext, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Theory.Model
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.structure_simpleGraphOfStructure · cited by 0Language.structure_simple…SimpleGraph.simpleGraphOfStructure · cited by 0SimpleGraph.simpleGraphOf…FirstOrder.Language.simpleGraphOfStructure_adj · cited by 0Language.simpleGraphOfStr…SimpleGraph · cited by 3072SimpleGraphMatrix.vecCons · cited by 852Matrix.vecConsMatrix.vecEmpty · cited by 832Matrix.vecEmptyFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Structure.RelMap · cited by 68Structure.RelMapFirstOrder.Language.Theory.Model · cited by 67Theory.ModelFirstOrder.Language.Theory.simpleGraph · cited by 4Theory.simpleGraphFirstOrder.Language.graph · cited by 4Language.graphFirstOrder.Language.adj · cited by 2Language.adjLanguage.simpleGraphOfStructu…CITED BYCITES

Cites9

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Cited by3

Results whose statement or proof uses this declaration.