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Theorems · Definition · order theory

OrderIso.dual

{α : Type u_2} → {β : Type u_3} → [inst : LE α] → [inst_1 : LE β] → α ≃o β → αᵒᵈ ≃o βᵒᵈ

An order isomorphism is also an order isomorphism between dual orders.

Defined in
Mathlib.Order.Hom.Basic
Cited by
24 results in Mathlib
Foundations
Depth 23 from the axioms · uses Quot.sound
Assumes
LELE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

OrderIso.isCoatom_iff · cited by 7OrderIso.isCoatom_iffIsGaloisGroup.intermediateFieldEquivSubgroup · cited by 6IsGaloisGroup.intermediat…MulChar.subgroupOrderIsoSubgroupMulChar · cited by 6MulChar.subgroupOrderIsoS…OrderIso.liminf_apply · cited by 6OrderIso.liminf_applyOrderIso.map_atBot · cited by 4OrderIso.map_atBotOrderIso.map_ciInf · cited by 4OrderIso.map_ciInfOrder.coheight_orderIso · cited by 4Order.coheight_orderIsoOrderIso.map_csInf' · cited by 4OrderIso.map_csInf'IsCyclotomicExtension.Rat.intermediateFieldEquivSubgroupChar · cited by 4Rat.intermediateFieldEqui…OrderIso.dual_apply · cited by 3OrderIso.dual_applyOrderIso.lowerBounds_image · cited by 2OrderIso.lowerBounds_imageOrderIso.comap_atBot · cited by 2OrderIso.comap_atBotOrderIso.tendsto_atBot_iff · cited by 2OrderIso.tendsto_atBot_iffOrderIso.isGLB_preimage · cited by 2OrderIso.isGLB_preimageOrderIso.isGLB_preimage' · cited by 2OrderIso.isGLB_preimage'OrderDual · cited by 927OrderDualOrderIso · cited by 874OrderIsoRelIso.toEquiv · cited by 113RelIso.toEquivOrderIso.le_iff_le · cited by 29OrderIso.le_iff_leOrderIso.dualCITED BYCITES

Cites4

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Cited by29

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