Theorems · Theorem · order theory
Set.InjOn.ne
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {f : α → β} {x y : α}, Set.InjOn f s → x ∈ s → y ∈ s → x ≠ y → f x ≠ f yAlias of the reverse direction of Set.InjOn.ne_iff.
- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.InjOnstatement and proof · cited by 543
- Set.InjOn.ne_iffproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- Finsupp.mapDomain_apply'proof · cited by 3
- StrictConvexOn.comp_convexOnproof · cited by 2
- Circle.disjoint_path_image_Iocproof · cited by 2
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2
- AddMonoidAlgebra.sum_ne_zero_of_injOn_supDegree'proof · cited by 1
- ChartedSpace.t1Spaceproof · cited by 1
- Set.InjOn.exists_mem_nhdsSetproof · cited by 1
- Finset.exists_equiv_extend_of_card_eqproof · cited by 1
- AddDissociated.randomisationproof · cited by 0