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Theorems · Theorem · order theory

Set.Nontrivial.coe_sort

∀ {α : Type u} {s : Set α}, s.Nontrivial → Nontrivial ↑s

Alias of the reverse direction of Set.nontrivial_coe_sort. s, 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
2 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Quot.sound
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Around this declaration

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

Set.nontrivial_mono · cited by 1Set.nontrivial_monoSimpleGraph.Subgraph.Preconnected.degree_zero_iff · cited by 0Preconnected.degree_zero_…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemNontrivial · cited by 2416NontrivialSet.Nontrivial · cited by 145Set.NontrivialSet.nontrivial_coe_sort · cited by 6Set.nontrivial_coe_sortNontrivial.coe_sortCITED BYCITES

Cites5

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Cited by2

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