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Theorems · Theorem · order theory

OrderIso.symm_apply_apply

∀ {α : Type u_2} {β : Type u_3} [inst : LE α] [inst_1 : LE β] (e : α ≃o β) (x : α), e.symm (e x) = x
Defined in
Mathlib.Order.Hom.Basic
Cited by
41 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, 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_inf · cited by 17OrderIso.map_infNNReal.sq_sqrt · cited by 9NNReal.sq_sqrtOrderIso.comap_atTop · cited by 6OrderIso.comap_atTopOrderIso.limsup_apply · cited by 5OrderIso.limsup_applyOrderIso.isAtom_iff · cited by 5OrderIso.isAtom_iffIdeal.ramificationIdx_pos · cited by 5Ideal.ramificationIdx_posOrderIso.complementedLattice · cited by 4OrderIso.complementedLatt…Real.arctan_tan · cited by 4Real.arctan_tanOrderIso.isLUB_image' · cited by 4OrderIso.isLUB_image'Submonoid.fg_iff_add_fg · cited by 3Submonoid.fg_iff_add_fgOrderIso.isCompl_iff · cited by 3OrderIso.isCompl_iffCategoryTheory.Pseudofunctor.IsPrestackFor.isSheafFor' · cited by 2IsPrestackFor.isSheafFor'AddSubgroup.toIntSubmodule_toAddSubgroup · cited by 2AddSubgroup.toIntSubmodul…AddSubmonoid.toNatSubmodule_toAddSubmonoid · cited by 2AddSubmonoid.toNatSubmodu…DFunLike.coe · cited by 62936DFunLike.coeOrderIso · cited by 874OrderIsoOrderIso.symm · cited by 475OrderIso.symmEquiv.symm_apply_apply · cited by 320Equiv.symm_apply_applyRelIso.toEquiv · cited by 113RelIso.toEquivOrderIso.symm_apply_applyCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by41

Results whose statement or proof uses this declaration.