Theorems · Theorem · order theory
Set.nontrivial_of_nontrivial_coe
∀ {α : Type u} {s : Set α}, Nontrivial ↑s → Nontrivial αA type with a set s whose coe_sort is a nontrivial type is nontrivial.
For the corresponding result for Subtype, see Subtype.nontrivial_iff_exists_ne.
- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
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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_of_nontrivialproof · cited by 1
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