OAI/MathematicalPhysics/NavierStokes/ForcedComputation/Programs/TorusGeometry.lean

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10 declarations, 0 contain sorry, 0 declared as axioms

The two-dimensional torus distance needed for support separation. Only the centered representative and its elementary triangle inequality are used; no geometric quotient machinery is required.

  1. def OAI.ForcedComputation.VelocityDetector.centeredRepresentative line 14
  2. def OAI.ForcedComputation.VelocityDetector.torusNorm line 18
  3. theorem OAI.ForcedComputation.VelocityDetector.centered_nearest_integer line 20
  4. theorem OAI.ForcedComputation.VelocityDetector.torusNorm_sq line 35
  5. theorem OAI.ForcedComputation.VelocityDetector.torusNorm_nonneg line 39
  6. theorem OAI.ForcedComputation.VelocityDetector.torusNorm_le_lattice line 41
  7. theorem OAI.ForcedComputation.VelocityDetector.torusNorm_le_norm line 52
  8. theorem OAI.ForcedComputation.VelocityDetector.torusNorm_add_le line 59
  9. theorem OAI.ForcedComputation.VelocityDetector.torusNorm_neg line 72
  10. theorem OAI.ForcedComputation.VelocityDetector.torus_separation line 84