OAI/Analysis/CircleDomains/Topology/RoundDiskSlices.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Horizontal chords of round complementary disks

The exact real interval cut out by a round disk is used to enumerate the holes of a chosen crossing segment. The formula includes tangent and radius-zero disks.

  1. def OAI.CircleDomainRigidity.horizontalChord line 17
  2. theorem OAI.CircleDomainRigidity.horizontalChord_nonneg line 21
  3. theorem OAI.CircleDomainRigidity.horizontalChord_valid line 28
  4. theorem OAI.CircleDomainRigidity.mem_closedBall_iff_mem_horizontalChord line 33
  5. theorem OAI.CircleDomainRigidity.horizontalChord_disjoint line 53
  6. theorem OAI.CircleDomainRigidity.horizontalChord_inside_segment line 66