Theorems · Theorem · group theory
Set.vadd_mem_vadd_set_iff
∀ {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : AddAction α β] {s : Set β} {a : α} {x : β},
a +ᵥ x ∈ a +ᵥ s ↔ x ∈ s- Cited by
- 10 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- Set.vaddSetstatement · cited by 403
- Function.Injective.mem_set_imageproof · cited by 53
- AddAction.injectiveproof · cited by 24
Cited by10
Results whose statement or proof uses this declaration.
- AddAction.mem_stabilizer_setproof · cited by 5
- geometric_hahn_banach_openproof · cited by 4
- ProperVAdd.isCompact_setOfPred_inter_nonemptyproof · cited by 2
- AddAction.IsBlock.isBlockSystemproof · cited by 1
- AddAction.IsBlock.stabilizer_leproof · cited by 1
- AddAction.IsBlock.orbit_stabilizer_eqproof · cited by 1
- AddAction.isMultiplyPreprimitive_succ_iff_ofStabilizerproof · cited by 0
- AffineSubspace.vadd_mem_pointwise_vadd_iffproof · cited by 0
- MeasureTheory.pairwise_disjoint_addFundamentalInteriorproof · cited by 0
- AddAction.le_stabilizer_iff_vadd_leproof · cited by 0