Mathlib Map

Theorems · Theorem · order theory

Finset.image_add_left_Ioo

∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedCancelAddMonoid α] [ExistsAddOfLE α]
  [inst_4 : LocallyFiniteOrder α] [inst_5 : DecidableEq α] (a b c : α),
  Finset.image (fun x => c + x) (Finset.Ioo a b) = Finset.Ioo (c + a) (c + b)
Defined in
Mathlib.Algebra.Order.Interval.Finset.Basic
Cited by
1 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidPartialOrderIsOrderedCancelAddMonoidExistsAddOfLELocallyFiniteOrderDecidableEq
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Around this declaration

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

Multiset.map_add_left_Ioo · cited by 1Multiset.map_add_left_IooDFunLike.coe · cited by 62936DFunLike.coeFinset · cited by 13712FinsetAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderFunction.Embedding · cited by 988Function.EmbeddingFinset.image · cited by 910Finset.imageLocallyFiniteOrder · cited by 658LocallyFiniteOrderIsOrderedCancelAddMonoid · cited by 359IsOrderedCancelAddMonoidExistsAddOfLE · cited by 330ExistsAddOfLEFinset.Ioo · cited by 185Finset.IooFinset.map_eq_image · cited by 50Finset.map_eq_imageaddLeftEmbedding · cited by 36addLeftEmbeddingadd_right_injective · cited by 36add_right_injectiveFunction.Embedding.coeFn_mk · cited by 19Embedding.coeFn_mkFinset.map_add_left_Ioo · cited by 1Finset.map_add_left_IooFinset.image_add_left_IooCITED BYCITES

Cites15

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Cited by1

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