openAI-math-dataset / lean /OAI /Probability /InvariantIsing /Magnetic /MagneticContinuationTwoJet.lean
| import OAI.Probability.InvariantIsing.Magnetic.MagneticContinuationJet | |
| namespace OAI | |
| /-! The variance generator requires only two derivatives of its bounded | |
| test. In particular it applies to the ordinary curvature without | |
| requiring a fifth derivative of the finite scalar field. -/ | |
| noncomputable section | |
| open MeasureTheory | |
| namespace InvariantIsing | |
| structure MagneticContinuationTwoJet where | |
| value : ℝ → ℝ | |
| first : ℝ → ℝ | |
| second : ℝ → ℝ | |
| mValue : Measurable value | |
| mFirst : Measurable first | |
| mSecond : Measurable second | |
| bValue : MagneticContinuationBound value | |
| bFirst : MagneticContinuationBound first | |
| bSecond : MagneticContinuationBound second | |
| dValue : ∀ z, HasDerivAt value (first z) z | |
| dFirst : ∀ z, HasDerivAt first (second z) z | |
| def MagneticContinuationJet.toTwoJet (P : MagneticContinuationJet) : | |
| MagneticContinuationTwoJet where | |
| value := P.value | |
| first := P.first | |
| second := P.second | |
| mValue := P.mValue | |
| mFirst := P.mFirst | |
| mSecond := P.mSecond | |
| bValue := P.bValue | |
| bFirst := P.bFirst | |
| bSecond := P.bSecond | |
| dValue := P.dValue | |
| dFirst := P.dFirst | |
| def MagneticContinuationJet.slopeTwoJet (P : MagneticContinuationJet) : | |
| MagneticContinuationTwoJet where | |
| value := P.first | |
| first := P.second | |
| second := P.third | |
| mValue := P.mFirst | |
| mFirst := P.mSecond | |
| mSecond := P.mThird | |
| bValue := P.bFirst | |
| bFirst := P.bSecond | |
| bSecond := P.bThird | |
| dValue := P.dFirst | |
| dFirst := P.dSecond | |
| end InvariantIsing | |
| end | |
| end OAI | |