`mkKernelHomEqProof`🔗

Definition

Construct the proof of equivalence between the original equality and the transformed one.

def

mkKernelHomEqProof (eqProofType lhs rhs : Lean.Expr)
  (proofs : List Lean.Expr) : Lean.MetaM Lean.Expr
mkKernelHomEqProof
  (eqProofType lhs rhs : Lean.Expr)
  (proofs : List Lean.Expr) :
  Lean.MetaM Lean.Expr

Code

def mkKernelHomEqProof (eqProofType lhs rhs : Expr) (proofs : List Expr) : MetaM Expr := do
  let mvar ← mkFreshExprSyntheticOpaqueMVar eqProofType
  let mvarId := mvar.mvarId!
  let propext := mkConst ``propext
  match ← mvarId.apply propext with
  | [mvarId] =>
    let proofs := proofs.reverse
    let mut mvarId := mvarId
    for proof in proofs do
      mvarId ← mvarId.nthRewrite 1 proof
    let (X, Y, xLvl, yLvl) ← getTypesFromKernel lhs
    let SX ← computeSFinkerOf X xLvl
    let SY ← computeSFinkerOf Y yLvl
    let e ← mkAppMInst ``hom_congr #[SX, SY, ← idME X, ← idME Y, lhs, rhs] 2
    unless ← isDefEq (← mvarId.getType) (← inferType e) do
      throwError "Type mismatch: expected {← mvarId.getType}, got {← inferType e}."
    mvarId.assign e
    instantiateMVars mvar
  | _ =>
    throwError "Failed to apply propext while building kernel_hom equivalence proof for
      {eqProofType}."

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: 6 project declarations, 144 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.

mkKernelHomEqProof🔗

`mkKernelHomEqProof`🔗