Prove2Me

`BookProof.NavierStokesFlow.nsFlow_energy_conserved` (t : ℝ) (psi : Fin n → ℂ) : star (nsFlowUnitary d t *ᵥ psi) ⬝ᵥ (nsHamiltonian d *ᵥ (nsFlowUnitary d t *ᵥ psi)) = star psi ⬝ᵥ (n

Proved
BookProof.NavierStokesFlow.nsFlow_energy_conserved

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesCauchy.

BookProof.NavierStokesFlow.nsFlow_energy_conserved (t : ℝ) (psi : Fin n → ℂ) : star (nsFlowUnitary d t *ᵥ psi) ⬝ᵥ (nsHamiltonian d *ᵥ (nsFlowUnitary d t *ᵥ psi)) = star psi ⬝ᵥ (nsHamiltonian d *ᵥ psi)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.nsFlow_energy_conserved.

Preamble
-- Generated from ChapterNavierStokesCauchy.lean — theorem BookProof.NavierStokesFlow.nsFlow_energy_conserved
import Mathlib
import Definitions.Def_ChapterNavierStokesCauchy
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow


open scoped BigOperators Matrix Matrix.Norms.Operator

variable {n : ℕ}
variable {n : ℕ} (d : NSTruncation n)
Formal statement
theorem BookProof.NavierStokesFlow.nsFlow_energy_conserved (t : ℝ) (psi : Fin n → ℂ) :
    star (nsFlowUnitary d t *ᵥ psi) ⬝ᵥ (nsHamiltonian d *ᵥ (nsFlowUnitary d t *ᵥ psi))
      = star psi ⬝ᵥ (nsHamiltonian d *ᵥ psi) := by sorry

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