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Theorems · Theorem · combinatorics

SimpleGraph.IsContained.trans

∀ {α : Type u_4} {β : Type u_5} {γ : Type u_6} {A : SimpleGraph α} {B : SimpleGraph β} {C : SimpleGraph γ},
  A.IsContained B → B.IsContained C → A.IsContained C

If A contains B and B contains C, then A contains C.

Defined in
Mathlib.Combinatorics.SimpleGraph.Copy
Cited by
9 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SimpleGraph.IsContained.trans' · cited by 5IsContained.trans'SimpleGraph.isContained_congr · cited by 5SimpleGraph.isContained_c…SimpleGraph.CliqueFree.comap · cited by 2CliqueFree.comapSimpleGraph.card_edgeFinset_deleteIncidenceSet_le_extremalNumber · cited by 1SimpleGraph.card_edgeFins…SimpleGraph.IsContained.mono_left · cited by 1IsContained.mono_leftSimpleGraph.IsContained.mono_right · cited by 1IsContained.mono_rightSimpleGraph.IsContained.not_cliqueFree_card · cited by 1IsContained.not_cliqueFre…SimpleGraph.isContained_top_iff · cited by 0SimpleGraph.isContained_t…SimpleGraph.IsContained.extremalNumber_le · cited by 0IsContained.extremalNumbe…SimpleGraph · cited by 3072SimpleGraphSimpleGraph.IsContained · cited by 68SimpleGraph.IsContainedSimpleGraph.Copy · cited by 49SimpleGraph.CopySimpleGraph.Copy.comp · cited by 5Copy.compIsContained.transCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.