Theorems · Definition · order theory
IndexedPartition.equivQuotient
{ι : Type u_1} → {α : Type u_2} → {s : ι → Set α} → (hs : IndexedPartition s) → ι ≃ hs.QuotientThe obvious equivalence between the quotient associated to an indexed partition and the indexing type.
- Defined in
- Mathlib.Data.Setoid.Partition
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Equivstatement · cited by 8,337
- Equiv.symmproof · cited by 3,681
- IndexedPartitionstatement and proof · cited by 33
- IndexedPartition.indexproof · cited by 22
- IndexedPartition.Quotientstatement · cited by 9
- IndexedPartition.someproof · cited by 5
- Setoid.quotientKerEquivOfRightInverseproof · cited by 2
- IndexedPartition.index_someproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- IndexedPartition.outproof · cited by 3
- IndexedPartition.equivQuotient_index_applystatement · cited by 1
- IndexedPartition.equivQuotient_indexstatement · cited by 0
- IndexedPartition.equivQuotient_symm_proj_applystatement · cited by 0
- IndexedPartition.proj_fiberstatement and proof · cited by 0