`BookProof.FockInteractionStability.gap_persists_pos` {mu a b : ℝ} (hmu : 0 < mu) (ha : a < 1) (hb : b < (1 - a) * mu) : 0 < (1 - a) * mu - b

Proved

BookProof.FockInteractionStability.gap_persists_pos

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockInteractionStability.

BookProof.FockInteractionStability.gap_persists_pos {mu a b : ℝ} (hmu : 0 < mu) (ha : a < 1) (hb : b < (1 - a) * mu) : 0 < (1 - a) * mu - b

Formalization note: Lean 4 identifier BookProof.FockInteractionStability.gap_persists_pos.

Preamble

-- Generated from ChapterFockInteractionStability.lean — theorem BookProof.FockInteractionStability.gap_persists_pos
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockNumberPreservingGap
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Mathlib
import Definitions.Def_ChapterFockInteractionStability
open BookProof.FockInteractionStability

variable {E : Type*} [NormedAddCommGroup E]


noncomputable section


open BookProof.FockSecondQuantization BookProof.FockOneParticleGap
open BookProof.FockNumberPreservingGap
open BookProof.FarisLavine BookProof.NavierStokesFlow

Formal statement

theorem BookProof.FockInteractionStability.gap_persists_pos {mu a b : ℝ} (hmu : 0 < mu) (ha : a < 1) (hb : b < (1 - a) * mu) :
    0 < (1 - a) * mu - b := by sorry

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