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Theorems · Theorem · order theory

Set.preimage_mul_const_Icc

∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] (a b c : α),
  (fun x => x * a) ⁻¹' Set.Icc b c = Set.Icc (b / a) (c / a)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by
3 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
CommGroupPartialOrderIsOrderedMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.image_div_const_Icc · cited by 0Set.image_div_const_IccSet.preimage_div_const_Icc · cited by 0Set.preimage_div_const_IccSet.image_const_div_Icc · cited by 0Set.image_const_div_IccSet · cited by 53352SetPartialOrder · cited by 6410PartialOrderSet.preimage · cited by 4946Set.preimageSet.Icc · cited by 1702Set.IccSet.Iic · cited by 1111Set.IicSet.Ici · cited by 1070Set.IciCommGroup · cited by 990CommGroupIsOrderedMonoid · cited by 577IsOrderedMonoidSet.preimage_mul_const_Iic · cited by 7Set.preimage_mul_const_IicSet.preimage_mul_const_Ici · cited by 5Set.preimage_mul_const_IciSet.preimage_mul_const_IccCITED BYCITES

Cites10

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Cited by3

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