Mathlib Map

Theorems · Theorem · order theory

Set.Nontrivial.ne_singleton

∀ {α : Type u} {s : Set α} {x : α}, s.Nontrivial → s ≠ {x}
Defined in
Mathlib.Data.Set.Subsingleton
Cited by
3 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.Nontrivial.not_subset_singleton · cited by 5Nontrivial.not_subset_sin…Set.nontrivial_iff_ne_singleton · cited by 2Set.nontrivial_iff_ne_sin…Matroid.IsCircuit.contractElem_isCircuit · cited by 0IsCircuit.contractElem_is…Set · cited by 53352SetSet.Nontrivial · cited by 145Set.NontrivialSet.not_nontrivial_singleton · cited by 1Set.not_nontrivial_single…Nontrivial.ne_singletonCITED BYCITES

Cites3

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

Cited by3

Results whose statement or proof uses this declaration.