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Theorems · Theorem · order theory

BddBelow.range_inv

∀ {G : Type u_2} [inst : Group G] [inst_1 : Preorder G] [MulLeftMono G] [MulRightMono G] {α : Type u_4} {f : α → G},
  BddBelow (Set.range f) → BddAbove (Set.range fun x => (f x)⁻¹)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Bounds
Cited by
1 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Quot.sound
Assumes
GroupPreorderMulLeftMonoMulRightMono
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Around this declaration

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

BddAbove.range_inv · cited by 0BddAbove.range_invPreorder · cited by 7952PreorderGroup · cited by 6238GroupSet.range · cited by 4705Set.rangeBddAbove · cited by 620BddAboveMulLeftMono · cited by 410MulLeftMonoBddBelow · cited by 401BddBelowMulRightMono · cited by 263MulRightMonoOrderIso.inv · cited by 27OrderIso.invOrderIso.monotone · cited by 23OrderIso.monotoneBddBelow.range_comp_left · cited by 3BddBelow.range_comp_leftBddBelow.range_invCITED BYCITES

Cites10

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Cited by1

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