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Theorems · Theorem · order theory

OrderIso.le_iff_le

∀ {α : Type u_2} {β : Type u_3} [inst : LE α] [inst_1 : LE β] (e : α ≃o β) {x y : α}, e x ≤ e y ↔ x ≤ y
Defined in
Mathlib.Order.Hom.Basic
Cited by
29 results in Mathlib
Foundations
Depth 22 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.map_sup · cited by 37OrderIso.map_supOrderIso.map_iInf · cited by 25OrderIso.map_iInfOrderIso.map_iSup · cited by 25OrderIso.map_iSupOrderIso.dual · cited by 24OrderIso.dualOrderIso.map_inf · cited by 17OrderIso.map_infNNReal.sqrt_le_sqrt · cited by 5NNReal.sqrt_le_sqrtOrderIso.preimage_Ici · cited by 5OrderIso.preimage_IciOrderIso.preimage_Iic · cited by 4OrderIso.preimage_IicIsDedekindDomain.idealFactorsEquivOfQuotEquiv_is_dvd_iso · cited by 3IsDedekindDomain.idealFac…Cardinal.preAleph_le_preAleph · cited by 2Cardinal.preAleph_le_preA…MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le · cited by 2MeasureTheory.integral_di…ExpGrowth.expGrowthInf_le_iff · cited by 2ExpGrowth.expGrowthInf_le…OrderIso.isBoundedUnder_ge_comp · cited by 2OrderIso.isBoundedUnder_g…OrderIso.isBoundedUnder_le_comp · cited by 2OrderIso.isBoundedUnder_l…ExpGrowth.expGrowthSup_le_iff · cited by 2ExpGrowth.expGrowthSup_le…DFunLike.coe · cited by 62936DFunLike.coeOrderIso · cited by 874OrderIsoRelIso.map_rel_iff · cited by 17RelIso.map_rel_iffOrderIso.le_iff_leCITED BYCITES

Cites3

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Cited by30

Results whose statement or proof uses this declaration.