`defaultConfig_props`

proved

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module: IndisputableMonolith.Gravity.ILG
domain: Gravity
line: 39 · github
papers citing: none yet

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IndisputableMonolith.Gravity.ILG on GitHub at line 39.

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depends on

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formal source

  36  eps_t_nonneg : 0 ≤ cfg.eps_t
  37  eps_t_le_one : cfg.eps_t ≤ 1
  38
  39@[simp] lemma defaultConfig_props : ConfigProps defaultConfig := by
  40  refine ⟨?h0, ?h1⟩ <;> norm_num
  41
  42def vbarSq_with (cfg : Config) (C : BaryonCurves) (r : ℝ) : ℝ :=
  43  max 0 ((C.vgas r) ^ 2 + ((Real.sqrt cfg.upsilonStar) * (C.vdisk r)) ^ 2 + (C.vbul r) ^ 2)
  44
  45def vbar_with (cfg : Config) (C : BaryonCurves) (r : ℝ) : ℝ :=
  46  Real.sqrt (max cfg.eps_v (vbarSq_with cfg C r))
  47
  48def gbar_with (cfg : Config) (C : BaryonCurves) (r : ℝ) : ℝ :=
  49  (vbar_with cfg C r) ^ 2 / max cfg.eps_r r
  50
  51structure Params where
  52  alpha      : ℝ
  53  Clag       : ℝ
  54  A          : ℝ
  55  r0         : ℝ
  56  p          : ℝ
  57  hz_over_Rd : ℝ
  58
  59structure ParamProps (P : Params) : Prop where
  60  alpha_nonneg : 0 ≤ P.alpha
  61  Clag_nonneg  : 0 ≤ P.Clag
  62  Clag_le_one  : P.Clag ≤ 1
  63  A_nonneg     : 0 ≤ P.A
  64  r0_pos       : 0 < P.r0
  65  p_pos        : 0 < P.p
  66
  67def w_t_with (cfg : Config) (P : Params) (Tdyn τ0 : ℝ) : ℝ :=
  68  let t := max cfg.eps_t (Tdyn / τ0)
  69  1 + P.Clag * (Real.rpow t P.alpha - 1)

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