Theorems · Theorem · logic and foundations
Subtype.coe_prop
∀ {α : Type u_1} {S : Set α} (a : { a // a ∈ S }), ↑a ∈ S- Defined in
- Mathlib.Data.Subtype
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- Subtype.propproof · cited by 505
Cited by42
Results whose statement or proof uses this declaration.
- multiset_prod_memproof · cited by 11
- multiset_sum_memproof · cited by 10
- list_sum_memproof · cited by 10
- list_prod_memproof · cited by 9
- Real.arctan_mem_Iooproof · cited by 7
- tsum_subtypeproof · cited by 6
- Real.arcsin_mem_Iccproof · cited by 4
- AddSubgroup.isComplement_iff_existsUnique_add_neg_memproof · cited by 3
- AddSubgroup.isComplement_iff_existsUnique_neg_add_memproof · cited by 2
- Real.ContinuousOn.circleAverageproof · cited by 2
- Set.domRestrict_extend_rangestatement · cited by 2
- SimpleGraph.Subgraph.IsMatching.exists_of_disjoint_sets_of_equivproof · cited by 2