Theorems · Theorem · order theory
Set.nontrivial_mono
∀ {α : Type u_1} {s t : Set α}, s ⊆ t → Nontrivial ↑s → Nontrivial ↑t- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Nontrivialstatement and proof · cited by 2,416
- Set.nontrivial_coe_sortproof · cited by 6
- Set.Nontrivial.monoproof · cited by 3
- Set.Nontrivial.coe_sortproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.nontrivial_max_triv_of_isNilpotentproof · cited by 2