Theorems · Theorem · order theory
Disjoint.preimage
∀ {α : Type u_1} {β : Type u_2} (f : α → β) {s t : Set β}, Disjoint s t → Disjoint (f ⁻¹' s) (f ⁻¹' t)- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 4,946
- Disjointstatement and proof · cited by 2,201
- disjoint_iff_inf_leproof · cited by 64
- Disjoint.le_botproof · cited by 52
Cited by22
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.preimageproof · cited by 5
- separated_by_continuousproof · cited by 4
- AddAction.IsBlock.preimageproof · cited by 3
- Set.preimage_eq_emptyproof · cited by 3
- measure_eq_measure_preimage_add_measure_tsum_Ico_zpowproof · cited by 2
- linearIndepOn_union_iffproof · cited by 2
- ProbabilityTheory.Kernel.measurable_kernel_prodMk_left_of_finiteproof · cited by 1
- measurable_measure_prodMk_left_finiteproof · cited by 1
- Set.Infinite.exists_union_disjoint_cardinal_eq_of_infiniteproof · cited by 1
- IsOpenMap.enatCard_connectedComponents_le_encard_preimage_singletonproof · cited by 1
- BoundedContinuousFunction.tietze_extension_stepproof · cited by 1
- MeasureTheory.Measure.countable_meas_level_set_pos₀proof · cited by 1