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Theorems · Theorem · order theory

OrderIso.apply_symm_apply

∀ {α : Type u_2} {β : Type u_3} [inst : LE α] [inst_1 : LE β] (e : α ≃o β) (x : β), e (e.symm x) = x
Defined in
Mathlib.Order.Hom.Basic
Cited by
45 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.

Real.tan_arctan · cited by 11Real.tan_arctanNNReal.sqrt_sq · cited by 7NNReal.sqrt_sqReal.exp_log_eq_abs · cited by 7Real.exp_log_eq_absOrderIso.preimage_Ici · cited by 5OrderIso.preimage_IciOrderIso.preimage_Iio · cited by 5OrderIso.preimage_IioOrderIso.preimage_Ioi · cited by 5OrderIso.preimage_IoiOrderIso.lt_symm_apply · cited by 4OrderIso.lt_symm_applyCategoryTheory.Sieve.overEquiv_iff · cited by 4Sieve.overEquiv_iffOrderIso.preimage_Iic · cited by 4OrderIso.preimage_IicReal.sin_arcsin' · cited by 3Real.sin_arcsin'OrderIso.symm_apply_lt · cited by 3OrderIso.symm_apply_ltSSet.stdSimplex.face_eq_ofSimplex · cited by 3stdSimplex.face_eq_ofSimp…OrderIso.isLUB_image · cited by 3OrderIso.isLUB_imageOrderIso.isLUB_preimage' · cited by 3OrderIso.isLUB_preimage'CategoryTheory.over_toGrothendieck_eq_toGrothendieck_comap_forget · cited by 3CategoryTheory.over_toGro…DFunLike.coe · cited by 62936DFunLike.coeOrderIso · cited by 874OrderIsoOrderIso.symm · cited by 475OrderIso.symmEquiv.apply_symm_apply · cited by 346Equiv.apply_symm_applyRelIso.toEquiv · cited by 113RelIso.toEquivOrderIso.apply_symm_applyCITED BYCITES

Cites5

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

Cited by45

Results whose statement or proof uses this declaration.