Mathlib Map

Theorems · Theorem · order theory

Set.image_add_const_Iio

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] (a b : α),
  (fun x => x + a) '' Set.Iio b = Set.Iio (b + a)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupPartialOrderIsOrderedAddMonoid
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Around this declaration

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

Set.Iio_add_bij · cited by 0Set.Iio_add_bijSet · cited by 53352SetAddCommGroup · cited by 12871AddCommGroupPartialOrder · cited by 6410PartialOrderSet.image · cited by 5609Set.imageIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidSet.Iio · cited by 1166Set.Iiosub_neg_eq_add · cited by 264sub_neg_eq_addSet.image_add_right · cited by 37Set.image_add_rightSet.preimage_add_const_Iio · cited by 9Set.preimage_add_const_IioSet.image_add_const_IioCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.