`BookProof.ChapterFreeFieldBornFiberTwo.two_le_bornFiber_card` {p : ↥(stdSimplex ℝ (Fin n))} : 2 ≤ Nat.card ↥(bornMapSphere n ⁻¹' {p})

Proved

BookProof.ChapterFreeFieldBornFiberTwo.two_le_bornFiber_card

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornFiberTwo.

BookProof.ChapterFreeFieldBornFiberTwo.two_le_bornFiber_card {p : ↥(stdSimplex ℝ (Fin n))} : 2 ≤ Nat.card ↥(bornMapSphere n ⁻¹' {p})

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornFiberTwo.two_le_bornFiber_card.

Preamble

-- Generated from ChapterFreeFieldBornFiberTwo.lean — theorem BookProof.ChapterFreeFieldBornFiberTwo.two_le_bornFiber_card
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSurj
import Definitions.Def_ChapterFreeFieldBornCont
import Definitions.Def_ChapterFreeFieldBornQuotient
import Definitions.Def_ChapterFreeFieldBornFiberCardGeneral
import Mathlib
import Definitions.Def_ChapterFreeFieldBornFiberTwo
open BookProof.ChapterFreeFieldBornFiberTwo


open MeasureTheory
open BookProof.ChapterFreeFieldBorn BookProof.ChapterFreeFieldBornSurj
open BookProof.ChapterFreeFieldBornCont BookProof.ChapterFreeFieldBornQuotient
open BookProof.ChapterFreeFieldBornFiberCardGeneral


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterFreeFieldBornFiberTwo.two_le_bornFiber_card {p : ↥(stdSimplex ℝ (Fin n))} :
    2 ≤ Nat.card ↥(bornMapSphere n ⁻¹' {p}) := by sorry

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