Theorems · Theorem · order theory
Partition.IsRepFun.apply_eq_apply_iff_rel
∀ {α : Type u_1} {u : Set α} {P : Partition u} {f : α → α} {a b : α}, P.IsRepFun f → a ∈ u → (f a = f b ↔ P.Rel a b)- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- by_contraproof · cited by 60
- Partition.Relstatement and proof · cited by 22
- Partition.IsRepFunstatement and proof · cited by 17
- Partition.IsRepFun.apply_of_notMemproof · cited by 7
- Partition.IsRepFun.rel_applyproof · cited by 4
- Partition.IsRepFun.apply_eq_applyproof · cited by 4
- Partition.Rel.transproof · cited by 2
- Partition.IsRepFun.apply_memproof · cited by 2
- Partition.rel_commproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Partition.IsRepFun.forall_apply_eq_apply_iffproof · cited by 1
- Partition.IsRepFun.idemproof · cited by 0
- Partition.IsRepFun.apply_eq_apply_iffproof · cited by 0