Theorems · Theorem · group theory
Set.preimage_add_left_singleton
∀ {α : Type u_2} [inst : AddGroup α] {a b : α}, (fun x => a + x) ⁻¹' {b} = {-a + b}- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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 · cited by 4,946
- AddGroupstatement and proof · cited by 4,410
- Set.image_singletonproof · cited by 174
- Set.image_add_left'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Filter.map_add_left_nhdsNEproof · cited by 1
- vadd_connectedComponentproof · cited by 1
- MeasureTheory.Measure.addHaar_singletonproof · cited by 1