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Theorems · Theorem · group theory

AddAction.toPerm_apply

∀ {α : Type u_5} {β : Type u_6} [inst : AddGroup α] [inst_1 : AddAction α β] (a : α) (x : β),
  (AddAction.toPerm a) x = a +ᵥ x
Defined in
Mathlib.Algebra.Group.Action.Basic
Cited by
4 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Quot.sound
Assumes
AddGroupAddAction
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Around this declaration

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

ProperVAdd.isCompact_setOfPred_inter_nonempty · cited by 2ProperVAdd.isCompact_setO…AddAction.toPerm_zero · cited by 1AddAction.toPerm_zeroSet.powersetCard.addAction_faithful · cited by 1powersetCard.addAction_fa…MeasureTheory.IsAddFundamentalDomain.vadd · cited by 0IsAddFundamentalDomain.va…DFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivAddGroup · cited by 4410AddGroupHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionAddAction.toPerm · cited by 21AddAction.toPermAddAction.toPerm_applyCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.