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Theorems · Theorem · combinatorics

SimpleGraph.ConnectedComponent.biUnion_supp_eq_supp

∀ {V : Type u} {G G' : SimpleGraph V},
  G ≤ G' → ∀ (c' : G'.ConnectedComponent), ⋃ c, ⋃ (_ : c.supp ⊆ c'.supp), c.supp = c'.supp
Defined in
Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
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Around this declaration

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

SimpleGraph.disjiUnion_supp_toFinset_eq_supp_toFinset · cited by 1SimpleGraph.disjiUnion_su…Set · cited by 53352SetSimpleGraph · cited by 3072SimpleGraphSet.iUnion · cited by 2483Set.iUnionSet.ext · cited by 2266Set.extSimpleGraph.ConnectedComponent · cited by 86SimpleGraph.ConnectedComp…SimpleGraph.ConnectedComponent.supp · cited by 42ConnectedComponent.suppSimpleGraph.connectedComponentMk · cited by 40SimpleGraph.connectedComp…SimpleGraph.ConnectedComponent.connectedComponentMk_supp_subset_supp · cited by 1ConnectedComponent.connec…ConnectedComponent.biUnion_su…CITED BYCITES

Cites8

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