`unliftId`🔗

Definition

Unlifts the identity kernel by unlifting the carrier type.

def

unliftId (e : Lean.Expr) (eLvl : Lean.Level) (proofs : List Lean.Expr) :
  Lean.MetaM (Lean.Expr × List Lean.Expr)
unliftId (e : Lean.Expr)
  (eLvl : Lean.Level)
  (proofs : List Lean.Expr) :
  Lean.MetaM (Lean.Expr × List Lean.Expr)

Code

def unliftId (e : Expr) (eLvl : Level) (proofs : List Expr) :
    MetaM (Expr × List Expr) := do
  unless e.isAppOf ``Kernel.id do
    throwError "Expected the identity kernel, but got {e}."
  let (X', _, _, _) ← getTypesFromKernel e
  let (X, xLvl) ← getOriginalType X'
  if X == X' then
    return (e, proofs)
  else
    let ex ← constructMeasurableEquiv X xLvl eLvl
    let id_unlift_proof ← mkAppM ``id_lift #[ex]
    let mX ← synthInstance (mkApp (mkConst ``MeasurableSpace [xLvl]) X)
    return (← mkAppOptM ``Kernel.id #[X, mX], id_unlift_proof :: proofs)

Actions: Source · Open Issue

Meaning last changed in v4.34.0-rc2-1-g439785b (2026-08-23).

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

Dependency graph

Audit surface: 3 project declarations, 118 external constants

✓ 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.

unliftId🔗

`unliftId`🔗