Theorems · Theorem · group theory
Set.nonempty_image_addRight_neg_inter_iff
∀ {α : Type u_2} [inst : SubtractionMonoid α] {s t : Set α} {a : α},
((fun x => x + -a) '' s ∩ t).Nonempty ↔ ((fun x => a + x) '' (-s) ∩ -t).Nonempty- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SubtractionMonoid
Around this declaration
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Cites12
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.imagestatement and proof · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- neg_negproof · cited by 960
- Set.image_congrproof · cited by 533
- neg_add_revproof · cited by 236
- SubtractionMonoidstatement and proof · cited by 208
- Set.negstatement · cited by 168
- Set.image_imageproof · cited by 140
- Set.image_neg_eq_negproof · cited by 52
- Set.inter_negproof · cited by 11
- Set.nonempty_negproof · cited by 5
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