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Theorems · Theorem · field theory

OrderRingHom.apply_eq_self

∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [Archimedean α] (f : α →+*o α)
  (x : α), f x = x
Defined in
Mathlib.Algebra.Order.Archimedean.Hom
Cited by
2 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRingArchimedean
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ArchimedeanClass.ofArchimedean_stdPart · cited by 1ArchimedeanClass.ofArchim…OrderRingIso.apply_eq_self · cited by 0OrderRingIso.apply_eq_selfDFunLike.coe · cited by 62936DFunLike.coeLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingArchimedean · cited by 603ArchimedeanOrderRingHom · cited by 132OrderRingHomOrderRingHom.id · cited by 11OrderRingHom.idOrderRingHom.eq_id · cited by 1OrderRingHom.eq_idOrderRingHom.apply_eq_selfCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.