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Theorems · Theorem · group theory

Set.vadd_set_compl

∀ {α : Type u_2} {β : Type u_3} [inst : AddGroup α] [inst_1 : AddAction α β] {s : Set β} {a : α}, a +ᵥ sᶜ = (a +ᵥ s)ᶜ
Defined in
Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
Cited by
2 results in Mathlib
Foundations
Depth 62 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.

AddAction.movedBy_mem_fixedBy_of_addCommute · cited by 2AddAction.movedBy_mem_fix…MeasureTheory.vadd_mem_ae · cited by 1MeasureTheory.vadd_mem_aeSet · cited by 53352SetAddGroup · cited by 4410AddGroupSet.univ · cited by 3945Set.univCompl.compl · cited by 2925Compl.complHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionSet.vaddSet · cited by 403Set.vaddSetSet.compl_eq_univ_sdiff · cited by 43Set.compl_eq_univ_sdiffSet.vadd_set_univ · cited by 16Set.vadd_set_univSet.vadd_set_sdiff · cited by 6Set.vadd_set_sdiffSet.vadd_set_complCITED BYCITES

Cites10

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Cited by2

Results whose statement or proof uses this declaration.