LeanMachineLearning

MeasurableEquiv.IicSuccProdπŸ”—

Definition

Measurable equivalence between a product up to n + 1 and the pair of the product up to n and the space at n + 1.

πŸ”—def
MeasurableEquiv.IicSuccProd.{u_3} (X : β„• β†’ Type u_3)
  [(n : β„•) β†’ MeasurableSpace (X n)] (n : β„•) :
  ((i : β†₯(Finset.Iic (n + 1))) β†’ X ↑i) ≃ᡐ
    ((i : β†₯(Finset.Iic n)) β†’ X ↑i) Γ— X (n + 1)
MeasurableEquiv.IicSuccProd.{u_3}
  (X : β„• β†’ Type u_3)
  [(n : β„•) β†’ MeasurableSpace (X n)]
  (n : β„•) :
  ((i : β†₯(Finset.Iic (n + 1))) β†’ X ↑i) ≃ᡐ
    ((i : β†₯(Finset.Iic n)) β†’ X ↑i) Γ—
      X (n + 1)

Code

def _root_.MeasurableEquiv.IicSuccProd (X : β„• β†’ Type*) [βˆ€ n, MeasurableSpace (X n)] (n : β„•) : MeasurableEquiv (Ξ  i : Iic (n + 1), X i) ((Ξ  i : Iic n, X i) Γ— X (n + 1)) := (MeasurableEquiv.IicProdIoc (Nat.le_succ n)).symm.trans (MeasurableEquiv.prodCongr (MeasurableEquiv.refl _) (MeasurableEquiv.piSingleton n).symm)

Actions: Source Β· Open Issue

Meaning unchanged since v4.33.0-rc1-29-gce231eb, the oldest revision on record (2026-07-30).

Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file Β· open it in the Lean web editor.

Dependency graph

Nothing to draw. Its statement rests on no other declaration in this project, and names nothing from a package left unaudited β€” so the graph is this declaration alone. That is the answer, not a missing picture.

Audit surface: 0 project declarations, 37 external constants

βœ“ Proved: no sorry anywhere in its closure

This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.