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Theorems · Theorem · order theory

Set.image_const_add_Ioo

∀ {M : Type u_1} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [IsOrderedCancelAddMonoid M] [ExistsAddOfLE M]
  (a b c : M), (fun x => a + x) '' Set.Ioo b c = Set.Ioo (a + b) (a + c)
Defined in
Mathlib.Algebra.Order.Interval.Set.Monoid
Cited by
1 results in Mathlib
Foundations
Depth 20 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.

Finset.map_add_left_Ioo · cited by 1Finset.map_add_left_IooSet · cited by 53352SetAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderSet.image · cited by 5609Set.imageadd_comm · cited by 1535add_commSet.Ioo · cited by 1214Set.IooSet.image_congr · cited by 533Set.image_congrIsOrderedCancelAddMonoid · cited by 359IsOrderedCancelAddMonoidExistsAddOfLE · cited by 330ExistsAddOfLESet.image_add_const_Ioo · cited by 3Set.image_add_const_IooSet.image_const_add_IooCITED BYCITES

Cites10

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Cited by1

Results whose statement or proof uses this declaration.