Theorems · Theorem · order theory
Set.nontrivial_coe_sort
∀ {α : Type u} {s : Set α}, Nontrivial ↑s ↔ s.Nontrivials, coerced to a type, is a nontrivial type if and only if s is a nontrivial set.
- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 2,416
- Set.Nontrivialstatement · cited by 145
Cited by6
Results whose statement or proof uses this declaration.
- Finset.one_lt_card_iff_nontrivialproof · cited by 6
- Set.powersetCard.nontrivialproof · cited by 2
- Set.Nontrivial.coe_sortproof · cited by 2
- MonoidWithZeroHom.range_nontrivialproof · cited by 1
- Set.nontrivial_monoproof · cited by 1
- Set.nontrivial_of_nontrivial_coeproof · cited by 0