Theorems · Theorem · logic and foundations
Set.nonempty_coe_sort
∀ {α : Type u} {s : Set α}, Nonempty ↑s ↔ s.Nonempty- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
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 · cited by 7,166
- Set.Nonemptystatement · cited by 2,627
- nonempty_subtypeproof · cited by 22
Cited by23
Results whose statement or proof uses this declaration.
- Set.Nonempty.coe_sortproof · cited by 6
- SimpleGraph.Subgraph.connected_iffproof · cited by 5
- finite_zmultiplesproof · cited by 3
- biInf_constproof · cited by 3
- sSup_symmDiff_leproof · cited by 3
- ringKrullDim_quotient_succ_le_of_nonZeroDivisorproof · cited by 3
- Summable.hasProdUniformlyOn_one_addproof · cited by 3
- biSup_constproof · cited by 2
- hasBasis_nhdsSet_Iic_Iioproof · cited by 2
- Cardinal.mk_set_ne_zero_iffproof · cited by 1
- upperBounds_prodproof · cited by 1
- AlgebraicGeometry.exists_mem_of_isClosed_of_nonemptyproof · cited by 1