recognition /
NavierStokes /
NavierStokes.DiscreteMaximumPrinciple /
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formal statement (Lean)
79 theorem one_step_factor_le_one (data : OneStepData)
80 (hsubK : data.subKolmogorov) :
81 1 + data.dt * (data.advectionBound - data.viscousRate) ≤ 1 := by
proof body
Term-mode proof.
82 have h1 : data.advectionBound - data.viscousRate ≤ 0 :=
83 sub_nonpos.mpr (advection_dominated_by_viscosity data hsubK)
84 linarith [mul_nonpos_of_nonneg_of_nonpos data.dt_pos.le h1]
85
86 /-- The gradient maximum is non-increasing under one NS time step when
87 the sub-Kolmogorov condition holds. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (16)
Lean names referenced from this declaration's body.
step
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in IndisputableMonolith.Foundation.ArithmeticFromLogic
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in IndisputableMonolith.Foundation.IntegersFromLogic
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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in IndisputableMonolith.Foundation.RationalsFromLogic
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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advection_dominated_by_viscosity
in IndisputableMonolith.NavierStokes.DiscreteMaximumPrinciple
decl_use
OneStepData
in IndisputableMonolith.NavierStokes.DiscreteMaximumPrinciple
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viscousRate
in IndisputableMonolith.NavierStokes.VortexStretching
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sub
in IndisputableMonolith.Numerics.Interval.Basic
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one
in IndisputableMonolith.QFT.SpinStatistics
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one
in IndisputableMonolith.RecogSpec.Core
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sub
in IndisputableMonolith.RecogSpec.Core
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gradient
in IndisputableMonolith.Relativity.Fields.Scalar
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