diff --git a/src/Lean/Compiler/Check.lean b/src/Lean/Compiler/Check.lean
index 0b48a6ca53..26164ec623 100644
--- a/src/Lean/Compiler/Check.lean
+++ b/src/Lean/Compiler/Check.lean
@@ -6,14 +6,15 @@ Authors: Leonardo de Moura
 import Lean.Compiler.InferType
 import Lean.Compiler.Util
 
-namespace Lean.Compiler.InferType
+namespace Lean.Compiler
+open InferType
 
 /-!
 Type checker for LCNF expressions
 -/
 
-structure Config where
-  terminalCasesOnly : Bool := false
+structure Check.Config where
+  terminalCasesOnly : Bool := true
 
 def lambdaBoundedTelescope (e : Expr) (n : Nat) (k : Array Expr → Expr → InferTypeM α) : InferTypeM α :=
   go e n #[]
@@ -26,7 +27,7 @@ where
         withLocalDecl n (d.instantiateRev xs) bi fun x => go b i (xs.push x)
       | _ => throwError "lambda expected"
 
-partial def check (e : Expr) (cfg : Config := {}) : InferTypeM Unit := do
+partial def check (e : Expr) (cfg : Check.Config := {}) : InferTypeM Unit := do
   checkBlock e #[]
 where
   checkBlock (e : Expr) (xs : Array Expr) : InferTypeM Unit := do
@@ -95,4 +96,4 @@ where
         unless compatibleTypes expectedType altBodyType do
           throwError "type mismatch at LCNF `cases` alternative{indentExpr altBody}\nhas type{indentExpr altBodyType}\nbut is expected to have type{indentExpr expectedType}"
 
-end Lean.Compiler.InferType
\ No newline at end of file
+end Lean.Compiler
\ No newline at end of file
diff --git a/src/Lean/Compiler/Decl.lean b/src/Lean/Compiler/Decl.lean
index 44454408b2..06ec342d04 100644
--- a/src/Lean/Compiler/Decl.lean
+++ b/src/Lean/Compiler/Decl.lean
@@ -61,8 +61,8 @@ def toDecl (declName : Name) : CoreM Decl := do
     let value ← toLCNF value -- TODO: uncomment
     return { name := declName, type, value }
 
-def Decl.check (decl : Decl) : CoreM Unit := do
-  InferType.check decl.value {} { lctx := {} }
+def Decl.check (decl : Decl) (cfg : Check.Config := {}): CoreM Unit := do
+  Compiler.check decl.value cfg { lctx := {} }
   let valueType ← InferType.inferType decl.value { lctx := {} }
   unless compatibleTypes decl.type valueType do
     throwError "declaration type mismatch at `{decl.name}`, value has type{indentExpr valueType}\nbut is expected to have type{indentExpr decl.type}"
diff --git a/src/Lean/Compiler/InferType.lean b/src/Lean/Compiler/InferType.lean
index 76c43cd8b7..13ccdff61f 100644
--- a/src/Lean/Compiler/InferType.lean
+++ b/src/Lean/Compiler/InferType.lean
@@ -155,6 +155,9 @@ instance : MonadInferType InferType.InferTypeM where
 
 export MonadInferType (inferType)
 
+instance [MonadLift m n] [MonadInferType m] : MonadInferType n where
+  inferType e := liftM (inferType e : m _)
+
 def getLevel [Monad m] [MonadInferType m] [MonadError m] (type : Expr) : m Level := do
   match (← inferType type) with
   | .sort u => return u
diff --git a/src/Lean/Compiler/Main.lean b/src/Lean/Compiler/Main.lean
index ad786bc16e..5095517b43 100644
--- a/src/Lean/Compiler/Main.lean
+++ b/src/Lean/Compiler/Main.lean
@@ -28,19 +28,18 @@ where
     let info ← getConstInfo declName
     Meta.isProp info.type <||> Meta.isTypeFormerType info.type
 
-def checkpoint (step : Name) (decls : Array Decl) : CoreM Unit := do
+def checkpoint (step : Name) (decls : Array Decl) (cfg : Check.Config := {}): CoreM Unit := do
   trace[Meta.debug] "After {step}"
   for decl in decls do
     withOptions (fun opts => opts.setBool `pp.motives.pi false) do
       trace[Meta.debug] "{decl.name} := {decl.value}"
-      decl.check
+      decl.check cfg
 
 def compile (declNames : Array Name) : CoreM Unit := do
   let declNames ← declNames.filterM shouldGenerateCode
   let decls ← declNames.mapM toDecl
-  checkpoint `init decls
-  -- TODO: uncomment
-  -- let decls ← decls.mapM (·.terminalCases)
-  -- checkpoint `terminalCases decls
+  checkpoint `init decls { terminalCasesOnly := false }
+  let decls ← decls.mapM (·.terminalCases)
+  checkpoint `terminalCases decls
 
 end Lean.Compiler
diff --git a/src/Lean/Compiler/TerminalCases.lean b/src/Lean/Compiler/TerminalCases.lean
index b1067004d5..31e2aed4ae 100644
--- a/src/Lean/Compiler/TerminalCases.lean
+++ b/src/Lean/Compiler/TerminalCases.lean
@@ -6,8 +6,7 @@ Authors: Leonardo de Moura
 import Lean.Meta.Check
 import Lean.Compiler.Util
 import Lean.Compiler.Decl
-
-#exit -- TODO: port file to new LCNF format
+import Lean.Compiler.CompilerM
 
 namespace Lean.Compiler
 
@@ -29,8 +28,8 @@ partial def visitAlt (e : Expr) (numParams : Nat) : M Expr := do
 partial def visitCases (casesInfo : CasesInfo) (cases : Expr) : M Expr := do
   let mut args := cases.getAppArgs
   if let some jp := (← read).jp? then
-    let .forallE _ _ b _ ← inferType' jp | unreachable! -- jp's type is guaranteed to be an nondependent arrow, see `visitLet`
-    args ← liftMetaM <| updateMotive casesInfo args b
+    let .forallE _ _ b _ ← inferType jp | unreachable! -- jp's type is guaranteed to be an nondependent arrow, see `visitLet`
+    args := casesInfo.updateResultingType args b
   for i in casesInfo.altsRange, numParams in casesInfo.altNumParams do
     args ← args.modifyM i (visitAlt · numParams)
   return mkAppN cases.getAppFn args
@@ -47,34 +46,15 @@ partial def visitLet (e : Expr) (fvars : Array Expr) : M Expr := do
     let type := type.instantiateRev fvars
     let mut value := value.instantiateRev fvars
     if let some casesInfo ← isCasesApp? value then
-      let (bodyAbst, safeJp) ← withNewScope do
+      let bodyAbst ← withNewScope do
         let x ← mkLocalDecl binderName type
         let body ← visitLet body (fvars.push x)
         let body ← mkLetUsingScope body
-        let bodyType ← inferType body
         let bodyAbst := body.abstract #[x]
-        if (bodyType.abstract #[x]).hasLooseBVars then
-          /-
-          We cannot eliminate this nonterminal `cases` because the resulting type of the joinpoint
-          depends on `x`. We have to wait until we perform erasure to do it.
-          -/
-          return (bodyAbst, false)
-        else if !(← liftMetaM <| Meta.isTypeCorrect body) then
-          /-
-          We cannot eliminate this nonterminal `cases` because the joinpoint is not type correct.
-          This can happen because we abstracted `x`.
-          We have to wait until we perform erasure to do it.
-          Remark: we can skip this test if we set `nonDep` properly.
-          -/
-          return (bodyAbst, false)
-        else
-          return (bodyAbst, true)
-      if !safeJp then
-        return .letE binderName type value bodyAbst nonDep
-      else
-        let jp ← mkJpDecl (.lam binderName type bodyAbst .default)
-        withReader (fun _ => { jp? := some jp }) do
-          visitCases casesInfo value
+        return bodyAbst
+      let jp ← mkJpDecl (.lam binderName type bodyAbst .default)
+      withReader (fun _ => { jp? := some jp }) do
+        visitCases casesInfo value
     else
       if value.isLambda then
         value ← visitLambda value
@@ -91,10 +71,10 @@ partial def visitLet (e : Expr) (fvars : Array Expr) : M Expr := do
         else
           return e
       | some jp =>
-        let .forallE _ d _ _ ← inferType' jp | unreachable!
+        let .forallE _ d _ _ ← inferType jp | unreachable!
         if isLcUnreachable e then
           mkLcUnreachable d
-        else if (← isDefEq (← inferType e) d) then
+        else if compatibleTypes (← inferType e) d then
           let x ← mkAuxLetDecl e
           return mkApp jp x
         else if let some x := isLcCast? e then
@@ -110,7 +90,7 @@ end
 end TerminalCases
 
 /--
-(Try to) ensure all `casesOn` and `matcher` applications are terminal.
+Ensure all `casesOn` and `matcher` applications are terminal.
 -/
 def Decl.terminalCases (decl : Decl) : CoreM Decl := do
   return { decl with value := (← TerminalCases.visitLambda decl.value |>.run {} |>.run' { nextIdx := (← getMaxLetVarIdx decl.value) + 1 }) }
diff --git a/src/Lean/Compiler/Util.lean b/src/Lean/Compiler/Util.lean
index e450bd8ddd..048ca754d3 100644
--- a/src/Lean/Compiler/Util.lean
+++ b/src/Lean/Compiler/Util.lean
@@ -89,6 +89,14 @@ def getCasesInfo? (declName : Name) : CoreM (Option CasesInfo) := do
 def CasesInfo.geNumDiscrs (casesInfo : CasesInfo) : Nat :=
   casesInfo.discrsRange.stop - casesInfo.discrsRange.start
 
+def CasesInfo.updateResultingType (casesInfo : CasesInfo) (casesArgs : Array Expr) (typeNew : Expr) : Array Expr :=
+  casesArgs.modify casesInfo.motivePos fun motive => go motive
+where
+  go (e : Expr) : Expr :=
+    match e with
+    | .lam n b d bi => .lam n b (go d) bi
+    | _ => typeNew
+
 def isCasesApp? (e : Expr) : CoreM (Option CasesInfo) := do
   let .const declName _ := e.getAppFn | return none
   if let some info ← getCasesInfo? declName then