Theorems · Theorem · order theory
Set.SurjOn.mono
∀ {α : Type u_1} {β : Type u_2} {s₁ s₂ : Set α} {t₁ t₂ : Set β} {f : α → β},
s₁ ⊆ s₂ → t₁ ⊆ t₂ → Set.SurjOn f s₁ t₂ → Set.SurjOn f s₂ t₁- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 17 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
- Set.Subset.transproof · cited by 218
- Set.image_monoproof · cited by 197
- Set.SurjOnstatement and proof · cited by 186
Cited by13
Results whose statement or proof uses this declaration.
- Ideal.height_le_height_add_spanFinrank_of_leproof · cited by 2
- IsAddFreimanHom.addRothNumber_monoproof · cited by 2
- Function.Surjective.surjOnproof · cited by 2
- Set.SurjOn.union_unionproof · cited by 2
- Set.surjOn_iUnion_iUnionproof · cited by 2
- PartialEquiv.surjective_of_target_eq_univproof · cited by 2
- Set.surjOn_iff_exists_bijOn_subsetproof · cited by 2
- Ideal.height_le_height_add_of_liesOverproof · cited by 1
- IsMulFreimanHom.mulRothNumber_monoproof · cited by 1
- ApproximatesLinearOn.open_imageproof · cited by 1
- Set.surjOn_iInter_iInterproof · cited by 1
- ApproximatesLinearOn.closedBall_subset_targetproof · cited by 0