Theorems · Theorem · group theory
Set.vadd_inter_nonempty_iff
∀ {α : Type u_2} [inst : AddGroup α] {s t : Set α} {x : α},
((x +ᵥ s) ∩ t).Nonempty ↔ ∃ a b, (a ∈ t ∧ b ∈ s) ∧ a + -b = x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.vaddSetstatement · cited by 403
- neg_add_cancel_rightproof · cited by 75
- add_neg_cancel_rightproof · cited by 65
- Set.mem_interproof · cited by 25
- Set.mem_vadd_setproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Set.vadd_inter_nonempty_iff'proof · cited by 1