LeanMachineLearning

ProbabilityTheory.Kernel.symm_IicSuccProd๐Ÿ”—

Lemma

No docstring.

๐Ÿ”—theorem
ProbabilityTheory.Kernel.symm_IicSuccProd.{u_2} {X : โ„• โ†’ Type u_2}
  [(n : โ„•) โ†’ MeasurableSpace (X n)] (n : โ„•) :
  MeasurableEquiv.symm (MeasurableEquiv.IicSuccProd X n) =
    MeasurableEquiv.trans
      (MeasurableEquiv.prodCongr
        (MeasurableEquiv.refl ((i : โ†ฅ(Finset.Iic n)) โ†’ X โ†‘i))
        (MeasurableEquiv.piSingleton n))
      (MeasurableEquiv.IicProdIoc โ‹ฏ)
ProbabilityTheory.Kernel.symm_IicSuccProd.{u_2}
  {X : โ„• โ†’ Type u_2}
  [(n : โ„•) โ†’ MeasurableSpace (X n)]
  (n : โ„•) :
  MeasurableEquiv.symm
      (MeasurableEquiv.IicSuccProd X n) =
    MeasurableEquiv.trans
      (MeasurableEquiv.prodCongr
        (MeasurableEquiv.refl
          ((i : โ†ฅ(Finset.Iic n)) โ†’ X โ†‘i))
        (MeasurableEquiv.piSingleton n))
      (MeasurableEquiv.IicProdIoc โ‹ฏ)

Code

lemma symm_IicSuccProd (n : โ„•) :
    (MeasurableEquiv.IicSuccProd X n).symm =
      (MeasurableEquiv.prodCongr (MeasurableEquiv.refl _) (MeasurableEquiv.piSingleton n)).trans
        (MeasurableEquiv.IicProdIoc (Nat.le_succ n))
Proof
rfl

Actions: Source ยท 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 ยท open it in the Lean web editor.

Dependency graph

Audit surface: 1 project declarations, 39 external constants

โœ“ 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.