`BookProof.FockFieldPerturbation.two_mul_sqrt_le` {c n N t : ℝ} (hN : 0 ≤ N) (ht : 0 < t) : 2 * c * Real.sqrt N * n ≤ t * N + c ^ 2 / t * n ^ 2

Proved

BookProof.FockFieldPerturbation.two_mul_sqrt_le

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockFieldPerturbation.

BookProof.FockFieldPerturbation.two_mul_sqrt_le {c n N t : ℝ} (hN : 0 ≤ N) (ht : 0 < t) : 2 * c * Real.sqrt N * n ≤ t * N + c ^ 2 / t * n ^ 2

Formalization note: Lean 4 identifier BookProof.FockFieldPerturbation.two_mul_sqrt_le.

Preamble

-- Generated from ChapterFockFieldPerturbation.lean — theorem BookProof.FockFieldPerturbation.two_mul_sqrt_le
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockNumberPreservingGap
import Definitions.Def_ChapterFockInteractionStability
import Mathlib
import Definitions.Def_ChapterFockFieldPerturbation
open BookProof.FockFieldPerturbation


noncomputable section


open BookProof.FockSecondQuantization BookProof.FockOneParticleGap
open BookProof.FockNumberPreservingGap BookProof.FockInteractionStability

Formal statement

theorem BookProof.FockFieldPerturbation.two_mul_sqrt_le {c n N t : ℝ} (hN : 0 ≤ N) (ht : 0 < t) :
    2 * c * Real.sqrt N * n ≤ t * N + c ^ 2 / t * n ^ 2 := by sorry

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