Theorems · Theorem · order theory
Set.MapsTo.mono_left
∀ {α : Type u_1} {β : Type u_2} {s₁ s₂ : Set α} {t : Set β} {f : α → β}, Set.MapsTo f s₁ t → s₂ ⊆ s₁ → Set.MapsTo f s₂ t- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 13 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 by13
Results whose statement or proof uses this declaration.
- ContMDiffWithinAt.compproof · cited by 18
- ContMDiffWithinAt.mpullbackWithin_vectorField_interproof · cited by 4
- Set.mapsTo_iInter_iInterproof · cited by 3
- MDifferentiableWithinAt.mpullbackWithin_vectorField_interproof · cited by 3
- LocallyLipschitz.compproof · cited by 3
- VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symmproof · cited by 3
- LipschitzOnWith.comp_locallyBoundedVariationOnproof · cited by 2
- Matroid.comapOn_dual_eq_of_bijOnproof · cited by 1
- CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_oneproof · cited by 1
- ContinuousMap.compactOpen_eq_generateFromproof · cited by 1
- continuousWithinAt_iff_sourceproof · cited by 1
- contDiffGroupoid_zero_eqproof · cited by 1