Theorems · Theorem · order theory
Partition.IsRepFun.apply_eq_apply
∀ {α : Type u_1} {u : Set α} {P : Partition u} {f : α → α}, P.IsRepFun f → ∀ ⦃a b : α⦄, P.Rel a b → f a = f bThe function maps related elements to the same representative.
- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Partitionstatement and proof · cited by 91
- Partition.Relstatement · cited by 22
- Partition.IsRepFunstatement and proof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- Partition.IsRepFun.apply_eq_apply_iff_relproof · cited by 3
- Partition.IsRepFun.apply_eq_apply_iff'proof · cited by 0
- Partition.IsRepFun.apply_applyproof · cited by 0
- Partition.IsRepFun.apply_eq_apply_iffproof · cited by 0