Theorems · Theorem · group theory

Set.subset_vadd_set_iff

∀ {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : AddAction α β] {A B : Set β} {a : α},
  A ⊆ a +ᵥ B ↔ -a +ᵥ A ⊆ B

Defined in: Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 16 from the axioms · uses propext, Quot.sound
Assumes: AddGroup AddAction

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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
Set.preimageproof · cited by 4,946
AddGroupstatement and proof · cited by 4,410
HVAdd.hVAddstatement and proof · cited by 1,820
AddActionstatement and proof · cited by 820
Set.vaddSetstatement · cited by 403
Set.image_subset_iffproof · cited by 203
Equiv.image_eq_preimage_symmproof · cited by 64
AddAction.toPermproof · cited by 21

Cited by3

Results whose statement or proof uses this declaration.

AddAction.isInvariantBlock_iff_isFixedBlockproof · cited by 1
isApproximateAddSubgroup_zeroproof · cited by 0
Finset.subset_vadd_finset_iffproof · cited by 0