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theorem proved term proof

subK_preserved

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formal statement (Lean)

  98theorem subK_preserved (data : OneStepData)
  99    (hsubK : data.subKolmogorov)
 100    (newGradMax : ℝ)
 101    (h_update : newGradMax ≤
 102      data.gradMax * (1 + data.dt * (data.advectionBound - data.viscousRate)))
 103    (newData : OneStepData)
 104    (h_same_params : newData.viscousRate = data.viscousRate)
 105    (h_new_grad : newData.gradMax = newGradMax) :
 106    newData.subKolmogorov := by

proof body

Term-mode proof.

 107  unfold OneStepData.subKolmogorov
 108  rw [h_new_grad, h_same_params]
 109  exact le_trans (gradient_nonincreasing data hsubK newGradMax h_update) hsubK
 110
 111/-! ## Inductive Propagation -/
 112
 113/-- The sub-Kolmogorov condition propagates through arbitrarily many
 114time steps by induction. -/

depends on (6)

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