openAI-math-dataset / lean /OAI /MathematicalPhysics /DefocusingNLS /Spectrum /SpectralBoundaryBound.lean
| import OAI.MathematicalPhysics.DefocusingNLS.Spectrum.SpectralCoupledBoundarySystem | |
| namespace OAI | |
| /-! Enlarging a Green constant preserves the constructed boundary system. -/ | |
| open Set | |
| namespace DefocusingNLS | |
| noncomputable def SpectralScalarBoundarySystem.withBound {R E A : ℝ} | |
| (S : SpectralScalarBoundarySystem R E A) (B : ℝ) (hAB : A ≤ B) : | |
| SpectralScalarBoundarySystem R E B := | |
| { S with | |
| green := fun r hr t ht => (S.green r hr t ht).trans | |
| (div_le_div_of_nonneg_right hAB (S.positive_k t ht).le) } | |
| end DefocusingNLS | |
| end OAI | |