Theorems · Theorem · group theory
Set.op_smul_inter_nonempty_iff
∀ {α : Type u_2} [inst : Group α] {s t : Set α} {x : αᵐᵒᵖ},
(x • s ∩ t).Nonempty ↔ ∃ a b, (a ∈ s ∧ b ∈ t) ∧ a⁻¹ * b = MulOpposite.unop x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Groupstatement and proof · cited by 6,238
- Set.Nonemptystatement and proof · cited by 2,627
- MulOppositestatement and proof · cited by 1,135
- Set.smulSetstatement · cited by 608
- MulOpposite.opproof · cited by 520
- MulOpposite.unopstatement and proof · cited by 268
- inv_mul_cancel_leftproof · cited by 88
- mul_inv_cancel_leftproof · cited by 86
- Set.mem_interproof · cited by 25
- Set.mem_smul_setproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.properlyDiscontinuousSMul_opposite_of_tendsto_cofiniteproof · cited by 0