Prove2Me

`BookProof.FockQuadratic.sig_tgt` {ω : ι → ℝ} {P Q a : Idx ι} (h : P ≤ a) : sig ω (tgt P Q a) = sig ω a - wsum ω P - deg P + wsum ω Q + deg Q

Proved
BookProof.FockQuadratic.sig_tgt

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockQuadraticEsa.

BookProof.FockQuadratic.sig_tgt {ω : ι → ℝ} {P Q a : Idx ι} (h : P ≤ a) : sig ω (tgt P Q a) = sig ω a - wsum ω P - deg P + wsum ω Q + deg Q

Formalization note: Lean 4 identifier BookProof.FockQuadratic.sig_tgt.

Preamble
-- Generated from ChapterFockQuadraticEsa.lean — theorem BookProof.FockQuadratic.sig_tgt
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterOperatorSeriesEsa
import Mathlib
import Definitions.Def_ChapterFockQuadraticEsa
import Definitions.Def_ChapterA3n
open BookProof.ChapterA3n
open BookProof.FockQuadratic

variable {ι : Type*}


open scoped ENNReal


open BookProof.FarisLavine BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.NavierStokesFlow.LpNat BookProof.OperatorSeries

noncomputable section
Formal statement
theorem BookProof.FockQuadratic.sig_tgt {ω : ι → ℝ} {P Q a : Idx ι} (h : P ≤ a) :
    sig ω (tgt P Q a) = sig ω a - wsum ω P - deg P + wsum ω Q + deg Q := by sorry

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