Theorems · Theorem · group theory
Set.op_vadd_inter_nonempty_iff
∀ {α : Type u_2} [inst : AddGroup α] {s t : Set α} {x : αᵃᵒᵖ},
((x +ᵥ s) ∩ t).Nonempty ↔ ∃ a b, (a ∈ s ∧ b ∈ t) ∧ -a + b = AddOpposite.unop x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- AddGroupstatement and proof · cited by 4,410
- Set.Nonemptystatement and proof · cited by 2,627
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddOppositestatement and proof · cited by 452
- Set.vaddSetstatement · cited by 403
- AddOpposite.opproof · cited by 192
- AddOpposite.unopstatement and proof · cited by 125
- neg_add_cancel_leftproof · cited by 84
- add_neg_cancel_leftproof · cited by 76
- Set.mem_interproof · cited by 25
- Set.mem_vadd_setproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.properlyDiscontinuousVAdd_opposite_of_tendsto_cofiniteproof · cited by 0