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Theorems · Theorem · group theory

Set.disjoint_vadd_set

∀ {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : AddAction α β] {s t : Set β} {a : α},
  Disjoint (a +ᵥ s) (a +ᵥ t) ↔ Disjoint s t
Defined in
Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddAction
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.disjoint_vadd_set_right · cited by 2Set.disjoint_vadd_set_rig…Set.disjoint_vadd_set_left · cited by 0Set.disjoint_vadd_set_leftSet · cited by 53352SetAddGroup · cited by 4410AddGroupDisjoint · cited by 2201DisjointHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionSet.vaddSet · cited by 403Set.vaddSetAddAction.injective · cited by 24AddAction.injectiveSet.disjoint_image_iff · cited by 6Set.disjoint_image_iffSet.disjoint_vadd_setCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.