Theorems · Theorem · combinatorics

Finpartition.mk_mem_nonUniforms

∀ {α : Type u_1} {𝕜 : Type u_2} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [inst_2 : DecidableEq α] {A : Finset α}
  (P : Finpartition A) (G : SimpleGraph α) [inst_3 : DecidableRel G.Adj] {ε : 𝕜} {u v : Finset α},
  (u, v) ∈ P.nonUniforms G ε ↔ u ∈ P.parts ∧ v ∈ P.parts ∧ u ≠ v ∧ ¬G.IsUniform ε u v

Defined in

Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderDecidableEqDecidableRel