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Theorems · Theorem · order theory

Set.image_add_const_Ioi

∀ {M : Type u_1} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [IsOrderedCancelAddMonoid M] [ExistsAddOfLE M]
  (a b : M), (fun x => x + a) '' Set.Ioi b = Set.Ioi (b + a)
Defined in
Mathlib.Algebra.Order.Interval.Set.Monoid
Cited by
1 results in Mathlib
Foundations
Depth 18 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_const_add_Ioi · cited by 0Set.image_const_add_IoiSet · cited by 53352SetAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSet.image · cited by 5609Set.imageSet.Ioi · cited by 1463Set.IoiIsOrderedCancelAddMonoid · cited by 359IsOrderedCancelAddMonoidExistsAddOfLE · cited by 330ExistsAddOfLESet.BijOn.image_eq · cited by 30BijOn.image_eqSet.Ioi_add_bij · cited by 3Set.Ioi_add_bijSet.image_add_const_IoiCITED BYCITES

Cites9

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Cited by1

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