Theorems · Theorem · combinatorics
Graph.toSimpleGraph_adj_iff
∀ {α : Type u_1} {β : Type u_2} {G : Graph α β} [G.Loopless] (u v : ↑G.vertexSet), G.toSimpleGraph.Adj u v ↔ G.Adj ↑u ↑v- Defined in
- Mathlib.Combinatorics.Graph.Simple
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Graph.Loopless
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraph.Adjstatement · cited by 1,346
- Graphstatement and proof · cited by 242
- Graph.vertexSetstatement and proof · cited by 87
- Graph.Adjstatement · cited by 23
- Graph.Looplessstatement and proof · cited by 12
- Graph.toSimpleGraphstatement · cited by 3
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