`rest_frame`

proved

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module: IndisputableMonolith.Physics.SpecialRelativityFromRS
domain: Physics
line: 31 · github
papers citing: none yet

open explainer

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IndisputableMonolith.Physics.SpecialRelativityFromRS on GitHub at line 31.

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All declarations in this module, on Recognition.

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depends on

used by

formal source

  28theorem srEffectCount : Fintype.card SREffect = 5 := by decide
  29
  30/-- Rest frame = recognition equilibrium: J = 0. -/
  31theorem rest_frame : Jcost 1 = 0 := Jcost_unit0
  32
  33/-- Motion has recognition cost: J > 0 off rest. -/
  34theorem motion_cost {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  35    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  36
  37/-- SR symmetry: J(β) = J(β⁻¹) (no preferred direction). -/
  38theorem sr_symmetry {r : ℝ} (hr : 0 < r) :
  39    Jcost r = Jcost r⁻¹ := Jcost_symm hr
  40
  41structure SpecialRelativityCert where
  42  five_effects : Fintype.card SREffect = 5
  43  rest_zero : Jcost 1 = 0
  44  motion_positive : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  45  symmetric : ∀ {r : ℝ}, 0 < r → Jcost r = Jcost r⁻¹
  46
  47def specialRelativityCert : SpecialRelativityCert where
  48  five_effects := srEffectCount
  49  rest_zero := rest_frame
  50  motion_positive := motion_cost
  51  symmetric := sr_symmetry
  52
  53end IndisputableMonolith.Physics.SpecialRelativityFromRS

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