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Theorems · Theorem · order theory

Set.image_add_const_Ioc

∀ {M : Type u_1} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [IsOrderedCancelAddMonoid M] [ExistsAddOfLE M]
  (a b c : M), (fun x => x + a) '' Set.Ioc b c = Set.Ioc (b + a) (c + a)
Defined in
Mathlib.Algebra.Order.Interval.Set.Monoid
Cited by
3 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidPartialOrderIsOrderedCancelAddMonoidExistsAddOfLE
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Around this declaration

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

Set.image_affine_Ioc · cited by 2Set.image_affine_IocSet.image_const_add_Ioc · cited by 1Set.image_const_add_IocFinset.map_add_right_Ioc · cited by 1Finset.map_add_right_IocSet · cited by 53352SetAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSet.image · cited by 5609Set.imageSet.Ioc · cited by 971Set.IocIsOrderedCancelAddMonoid · cited by 359IsOrderedCancelAddMonoidExistsAddOfLE · cited by 330ExistsAddOfLESet.BijOn.image_eq · cited by 30BijOn.image_eqSet.Ioc_add_bij · cited by 1Set.Ioc_add_bijSet.image_add_const_IocCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.