Mathlib Map

Theorems · Theorem · order theory

Set.image_div_const_Ioi

∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] (a b : α),
  (fun x => x / a) '' Set.Ioi b = Set.Ioi (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
CommGroupPartialOrderIsOrderedMonoid
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Around this declaration

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

Filter.map_divRight_nhdsGT · cited by 0Filter.map_divRight_nhdsGTSet · cited by 53352SetPartialOrder · cited by 6410PartialOrderSet.image · cited by 5609Set.imageSet.preimage · cited by 4946Set.preimageSet.Ioi · cited by 1463Set.IoiCommGroup · cited by 990CommGroupdiv_eq_mul_inv · cited by 715div_eq_mul_invIsOrderedMonoid · cited by 577IsOrderedMonoidSet.image_congr · cited by 533Set.image_congrinv_inv · cited by 494inv_invSet.image_mul_right · cited by 24Set.image_mul_rightSet.preimage_mul_const_Ioi · cited by 7Set.preimage_mul_const_IoiSet.image_div_const_IoiCITED BYCITES

Cites12

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Cited by1

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