OAI/Combinatorics/Progressions/Estimates/AmplificationFinalCostGrowth.lean

GitHub source file

33 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.Erdos3.amplificationGain line 11
  2. theorem OAI.Erdos3.amplificationGain_closed line 15
  3. theorem OAI.Erdos3.amplificationGain_pos line 24
  4. theorem OAI.Erdos3.amplificationGain_tendsto line 29
  5. theorem OAI.Erdos3.exists_amplificationGain_mul_ge_one line 39
  6. def OAI.Erdos3.amplificationResource line 46
  7. theorem OAI.Erdos3.amplificationResource_ge_two line 50
  8. theorem OAI.Erdos3.amplificationResource_room line 65
  9. theorem OAI.Erdos3.log_amplificationResource_le line 71
  10. theorem OAI.Erdos3.pow_log_exchange line 107
  11. theorem OAI.Erdos3.pow_floor_log_le line 113
  12. theorem OAI.Erdos3.div_le_pow_floor_log line 120
  13. def OAI.Erdos3.levelCoefficient line 131
  14. def OAI.Erdos3.gainExponent line 133
  15. def OAI.Erdos3.potentialExponent line 135
  16. theorem OAI.Erdos3.levelCoefficient_pos line 137
  17. theorem OAI.Erdos3.levelCoefficient_mul_log line 141
  18. theorem OAI.Erdos3.gainExponent_pos_le_quarter line 147
  19. theorem OAI.Erdos3.potentialExponent_bounds line 157
  20. theorem OAI.Erdos3.resource_base_at_selected_level line 168
  21. theorem OAI.Erdos3.gain_base_at_selected_level line 173
  22. theorem OAI.Erdos3.amplificationResource_add_two_le_succ line 188
  23. theorem OAI.Erdos3.amplificationResource_strictMono line 196
  24. theorem OAI.Erdos3.amplificationResource_monotone line 204
  25. theorem OAI.Erdos3.amplificationResource_zero_le line 209
  26. theorem OAI.Erdos3.amplificationResource_parameter_le_zero line 214
  27. theorem OAI.Erdos3.amplificationResource_parameter_le line 221
  28. theorem OAI.Erdos3.amplificationResource_max_threshold_le line 227
  29. theorem OAI.Erdos3.amplificationResource_max_nat_threshold_le line 234
  30. theorem OAI.Erdos3.amplificationFinalCost_one_le line 248
  31. theorem OAI.Erdos3.amplificationFinalCost_add_two_le line 255
  32. theorem OAI.Erdos3.amplificationFinalCost_resource_le line 263
  33. theorem OAI.Erdos3.amplificationFinalCost_pos line 269