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7d9f027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | import Mathlib
import OAI.Probability.SKGap.Stability.OrdinaryClosure
import OAI.Probability.SKGap.Localization.RecipeCoefficientClosure
namespace OAI
section
noncomputable section
open scoped BigOperators
namespace SKGapCutoff.Recipe
open SKGap.Noncrossing.Primary
variable {n : ℕ} {ι κ σ τ : Type*} [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] [Fintype σ] [Fintype τ]
namespace LocalConstants
def withCoefficient (c : LocalConstants) (K S : ℝ) (hK : 1≤K) (hS : 0≤S) : LocalConstants :=
{c with A:=K,C:=K,S:=S,one_le_A:=hK,C_nonneg:=le_trans (by norm_num) hK,C_le_A:=le_rfl,S_nonneg:=hS}
end LocalConstants
theorem LocalOrdinaryInput.with_coefficients {D : OrdinaryData n ι κ σ} {N : ℕ}
{T : ι→SourceTree (Fin n→ℝ)} {x : Spin n} {c : LocalConstants}
(h : LocalOrdinaryInput D T x N c) (E : OrdinaryData n ι κ τ)
(hJ : E.J=D.J) (hj : E.j=D.j) (hH : E.H=D.H) (hp : E.predecessor=D.predecessor) (hθ : E.θ=D.θ)
(A : ℕ) (K S : ℝ) (hK : 1≤K) (hS : 0≤S)
(hs : (∑s,vectorNorm (E.seed s))≤S) (hc : E.CoefficientClass A x K) :
LocalOrdinaryInput E T x A (c.withCoefficient K S hK hS) := by
refine ⟨h.dimension,?_,?_,?_,?_,?_,?_,hs,?_,hc.seedRegular,hc.auxRegular,?_,?_⟩
· simpa only [hJ,LocalConstants.withCoefficient] using h.interaction
· simpa only [hH,LocalConstants.withCoefficient] using h.primaryShape
· simpa only [hH,hj,hJ,LocalConstants.withCoefficient] using h.primaryFieldError
· simpa only [hp,hj,hJ,LocalConstants.withCoefficient] using h.primarySourceError
· simpa only [hp] using h.primaryValue
· simpa only [hp,LocalConstants.withCoefficient] using h.primaryDerivative
· simpa only [hθ,LocalConstants.withCoefficient] using h.parameter
· intro a ha s i; exact (hc.seedValue a ha s).at i
· intro a ha b i; exact (hc.auxValue a ha b).at i
end SKGapCutoff.Recipe
end
end
end OAI
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