Theorems · Theorem · logic and foundations
Set.mapsTo_preimage
∀ {α : Type u} {β : Type v} (f : α → β) (t : Set β), Set.MapsTo f (f ⁻¹' t) t- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 5 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.preimagestatement · cited by 4,946
- Set.MapsTostatement · cited by 732
Cited by36
Results whose statement or proof uses this declaration.
- Set.restrictPreimageproof · cited by 84
- ContMDiffWithinAt.compproof · cited by 18
- Continuous.restrictPreimageproof · cited by 9
- ContMDiffWithinAt.mpullbackWithin_vectorField_interproof · cited by 4
- HasLineDerivWithinAt.smulproof · cited by 3
- MDifferentiableWithinAt.mpullbackWithin_vectorField_interproof · cited by 3
- IsOpenQuotientMap.dense_preimage_iffproof · cited by 3
- VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symmproof · cited by 3
- ContinuousLinearEquiv.comp_right_differentiableWithinAt_iffproof · cited by 3
- ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iffproof · cited by 3
- LocallyLipschitz.compproof · cited by 3
- smul_preimage_set_subsetₛₗproof · cited by 2