Mathlib Map

Theorems · Theorem · general topology

Circle.disjoint_path_image_Ioc

∀ {x y : Circle}, x ≠ y → Disjoint (⇑(x.path y) '' Set.Ioc 0 1) (⇑(y.path x) '' Set.Ioc 0 1)
Defined in
Mathlib.Analysis.SpecialFunctions.Complex.Circle
Cited by
2 results in Mathlib
Foundations
Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Circle.range_path_inter_range_path · cited by 2Circle.range_path_inter_r…Circle.compl_path_image_Ioc · cited by 1Circle.compl_path_image_I…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealSet.Elem · cited by 7166Set.ElemSet.image · cited by 5609Set.imageDisjoint · cited by 2201DisjointReal.pi · cited by 1774Real.piSet.Ioc · cited by 971Set.IocunitInterval · cited by 607unitIntervalPath · cited by 318PathCircle · cited by 227CircleComplex.arg · cited by 220Complex.argadd_sub_cancel_left · cited by 198add_sub_cancel_leftCircle.exp · cited by 73Circle.expCircle.angleDiff · cited by 17Circle.angleDiffCircle.disjoint_path_image_IocCITED BYCITES

Cites22

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

  • DFunLike.coestatement and proof · cited by 62,936
  • Setstatement and proof · cited by 53,352
  • Realstatement and proof · cited by 25,697
  • Set.Elemstatement · cited by 7,166
  • Set.imagestatement and proof · cited by 5,609
  • Disjointstatement and proof · cited by 2,201
  • Real.piproof · cited by 1,774
  • Set.Iocstatement and proof · cited by 971
  • unitIntervalstatement · cited by 607
  • Pathstatement · cited by 318
  • Circlestatement and proof · cited by 227
  • Complex.argproof · cited by 220

Cited by2

Results whose statement or proof uses this declaration.