Theorems · Theorem · order theory
Set.forall_mem_image
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set α} {p : β → Prop}, (∀ y ∈ f '' s, p y) ↔ ∀ ⦃x : α⦄, x ∈ s → p (f x)- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
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.
Cited by65
Results whose statement or proof uses this declaration.
- Set.image_subset_iffproof · cited by 203
- IsCompact.exists_isMinOnproof · cited by 15
- Monotone.mem_upperBounds_imageproof · cited by 12
- Monotone.mem_lowerBounds_imageproof · cited by 11
- Set.Finite.isOpen_biInterproof · cited by 10
- Set.image_subset_image2_rightproof · cited by 8
- MeasureTheory.Measure.restrict_sub_eq_restrict_sub_restrictproof · cited by 6
- induced_generateFrom_eqproof · cited by 5
- Set.image_subset_image2_leftproof · cited by 5
- AmpleSet.imageproof · cited by 4
- MonotoneOn.mem_lowerBounds_imageproof · cited by 4
- MonotoneOn.mem_upperBounds_imageproof · cited by 4