`BookProof.ChapterFreeFieldBornFiberCardGeneral.bornFiber_card_general_inc` {p : ↥(stdSimplex ℝ (Fin n))} : Nat.card ↥(bornMapSphere n ⁻¹' {p}) = 2 ^ (posSupport (p : Fin n → ℝ)).card

Proved

BookProof.ChapterFreeFieldBornFiberCardGeneral.bornFiber_card_general_inc

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornFiberCardGeneral.

BookProof.ChapterFreeFieldBornFiberCardGeneral.bornFiber_card_general_inc {p : ↥(stdSimplex ℝ (Fin n))} : Nat.card ↥(bornMapSphere n ⁻¹' {p}) = 2 ^ (posSupport (p : Fin n → ℝ)).card

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornFiberCardGeneral.bornFiber_card_general_inc.

Replaces the unuploadable node BookProof_ChapterFreeFieldBornFiberCardGeneral_bornFiber_card_general, whose statement name is already declared inside its published definition bundle; the _inc suffix publishes the same statement as its own node.

Preamble

-- Generated from ChapterFreeFieldBornFiberCardGeneral.lean — theorem BookProof.ChapterFreeFieldBornFiberCardGeneral.bornFiber_card_general_inc
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSurj
import Definitions.Def_ChapterFreeFieldBornCont
import Definitions.Def_ChapterFreeFieldBornSignGauge
import Definitions.Def_ChapterFreeFieldBornSignFiber
import Definitions.Def_ChapterFreeFieldBornSectionBij
import Definitions.Def_ChapterFreeFieldBornQuotient
import Definitions.Def_ChapterFreeFieldBornFiberCard
import Mathlib
import Definitions.Def_ChapterFreeFieldBornFiberCardGeneral
open BookProof.ChapterFreeFieldBornFiberCardGeneral


open MeasureTheory
open BookProof.ChapterFreeFieldBorn BookProof.ChapterFreeFieldBornSurj
open BookProof.ChapterFreeFieldBornCont BookProof.ChapterFreeFieldBornSignGauge
open BookProof.ChapterFreeFieldBornSignFiber BookProof.ChapterFreeFieldBornSectionBij
open BookProof.ChapterFreeFieldBornQuotient BookProof.ChapterFreeFieldBornFiberCard


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterFreeFieldBornFiberCardGeneral.bornFiber_card_general_inc {p : ↥(stdSimplex ℝ (Fin n))} :
    Nat.card ↥(bornMapSphere n ⁻¹' {p}) = 2 ^ (posSupport (p : Fin n → ℝ)).card := by sorry

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