Theorems · Theorem · order theory
Set.MapsTo.mono
∀ {α : Type u_1} {β : Type u_2} {s₁ s₂ : Set α} {t₁ t₂ : Set β} {f : α → β},
Set.MapsTo f s₁ t₁ → s₂ ⊆ s₁ → t₁ ⊆ t₂ → Set.MapsTo f s₂ t₂- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.MapsTostatement and proof · cited by 732
Cited by16
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_deriv_smul_comp'''proof · cited by 4
- HasFDerivWithinAt.uniqueDiffWithinAtproof · cited by 3
- IsOpenMap.mapsTo_interiorproof · cited by 3
- IsAddFreimanHom.addRothNumber_monoproof · cited by 2
- Complex.norm_eqOn_closedBall_of_isMaxOnproof · cited by 2
- Set.mapsTo_interproof · cited by 2
- BoxIntegral.hasIntegral_GP_pderivproof · cited by 1
- IsAddFreimanIso.addRothNumber_congrproof · cited by 1
- IsMulFreimanHom.mulRothNumber_monoproof · cited by 1
- Set.mapsTo_rangeproof · cited by 1
- ContinuousOn.tendsto_nhdsSetproof · cited by 1
- ContinuousMap.compactOpen_eq_generateFromproof · cited by 1