diff --git a/src/Lean/Meta/Tactic/Grind.lean b/src/Lean/Meta/Tactic/Grind.lean
index 92019df59e..938341c3ec 100644
--- a/src/Lean/Meta/Tactic/Grind.lean
+++ b/src/Lean/Meta/Tactic/Grind.lean
@@ -7,7 +7,6 @@ prelude
 import Lean.Meta.Tactic.Grind.Attr
 import Lean.Meta.Tactic.Grind.RevertAll
 import Lean.Meta.Tactic.Grind.Types
-import Lean.Meta.Tactic.Grind.Preprocessor
 import Lean.Meta.Tactic.Grind.Util
 import Lean.Meta.Tactic.Grind.Cases
 import Lean.Meta.Tactic.Grind.Injection
@@ -22,6 +21,9 @@ import Lean.Meta.Tactic.Grind.Simp
 import Lean.Meta.Tactic.Grind.Ctor
 import Lean.Meta.Tactic.Grind.Parser
 import Lean.Meta.Tactic.Grind.EMatchTheorem
+import Lean.Meta.Tactic.Grind.EMatch
+import Lean.Meta.Tactic.Grind.Main
+
 
 namespace Lean
 
@@ -41,8 +43,8 @@ builtin_initialize registerTraceClass `grind.simp
 builtin_initialize registerTraceClass `grind.debug
 builtin_initialize registerTraceClass `grind.debug.proofs
 builtin_initialize registerTraceClass `grind.debug.congr
-builtin_initialize registerTraceClass `grind.debug.pre
 builtin_initialize registerTraceClass `grind.debug.proof
 builtin_initialize registerTraceClass `grind.debug.proj
+builtin_initialize registerTraceClass `grind.debug.parent
 
 end Lean
diff --git a/src/Lean/Meta/Tactic/Grind/Core.lean b/src/Lean/Meta/Tactic/Grind/Core.lean
index 57a58499dc..0a80f7e753 100644
--- a/src/Lean/Meta/Tactic/Grind/Core.lean
+++ b/src/Lean/Meta/Tactic/Grind/Core.lean
@@ -41,6 +41,7 @@ This is an auxiliary function performed while merging equivalence classes.
 private def removeParents (root : Expr) : GoalM ParentSet := do
   let parents ← getParentsAndReset root
   for parent in parents do
+    trace[grind.debug.parent] "remove: {parent}"
     modify fun s => { s with congrTable := s.congrTable.erase { e := parent } }
   return parents
 
@@ -50,6 +51,7 @@ This is an auxiliary function performed while merging equivalence classes.
 -/
 private def reinsertParents (parents : ParentSet) : GoalM Unit := do
   for parent in parents do
+    trace[grind.debug.parent] "reinsert: {parent}"
     addCongrTable parent
 
 /-- Closes the goal when `True` and `False` are in the same equivalence class. -/
@@ -223,10 +225,8 @@ where
       internalize rhs generation
       addEqCore lhs rhs proof isHEq
 
-/--
-Adds a new hypothesis.
--/
-def addHyp (fvarId : FVarId) (generation := 0) : GoalM Unit := do
+/-- Adds a new hypothesis. -/
+def addHypothesis (fvarId : FVarId) (generation := 0) : GoalM Unit := do
   add (← fvarId.getType) (mkFVar fvarId) generation
 
 end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/EMatch.lean b/src/Lean/Meta/Tactic/Grind/EMatch.lean
index 69e24b606c..762048e120 100644
--- a/src/Lean/Meta/Tactic/Grind/EMatch.lean
+++ b/src/Lean/Meta/Tactic/Grind/EMatch.lean
@@ -5,7 +5,7 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Lean.Meta.Tactic.Grind.Types
-import Lean.Meta.Tactic.Grind.Internalize
+import Lean.Meta.Tactic.Grind.Intro
 
 namespace Lean.Meta.Grind
 namespace EMatch
@@ -278,4 +278,15 @@ def ematch : GoalM Unit := do
       gmt          := s.gmt + 1
     }
 
+/-- Performs one round of E-matching, and assert new instances. -/
+def ematchAndAssert? (goal : Goal) : GrindM (Option (List Goal)) := do
+  let numInstances := goal.numInstances
+  let goal ← GoalM.run' goal ematch
+  if goal.numInstances == numInstances then
+    return none
+  assertAll goal
+
+def ematchStar (goal : Goal) : GrindM (List Goal) := do
+  iterate goal ematchAndAssert?
+
 end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/ForallProp.lean b/src/Lean/Meta/Tactic/Grind/ForallProp.lean
index d6c42053ea..9228fe6713 100644
--- a/src/Lean/Meta/Tactic/Grind/ForallProp.lean
+++ b/src/Lean/Meta/Tactic/Grind/ForallProp.lean
@@ -20,7 +20,7 @@ def propagateForallProp (parent : Expr) : GoalM Unit := do
   unless (← isEqTrue p) do return ()
   let h₁ ← mkEqTrueProof p
   let qh₁ := q.instantiate1 (mkApp2 (mkConst ``of_eq_true) p h₁)
-  let r ← pre qh₁
+  let r ← simp qh₁
   let q := mkLambda n bi p q
   let q' := r.expr
   internalize q' (← getGeneration parent)
diff --git a/src/Lean/Meta/Tactic/Grind/Intro.lean b/src/Lean/Meta/Tactic/Grind/Intro.lean
new file mode 100644
index 0000000000..00438e1042
--- /dev/null
+++ b/src/Lean/Meta/Tactic/Grind/Intro.lean
@@ -0,0 +1,139 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Grind.Lemmas
+import Lean.Meta.Tactic.Assert
+import Lean.Meta.Tactic.Grind.Simp
+import Lean.Meta.Tactic.Grind.Types
+import Lean.Meta.Tactic.Grind.Cases
+import Lean.Meta.Tactic.Grind.Injection
+import Lean.Meta.Tactic.Grind.Core
+
+namespace Lean.Meta.Grind
+
+private inductive IntroResult where
+  | done
+  | newHyp (fvarId : FVarId) (goal : Goal)
+  | newDepHyp (goal : Goal)
+  | newLocal (fvarId : FVarId) (goal : Goal)
+  deriving Inhabited
+
+private def introNext (goal : Goal) : GrindM IntroResult := do
+  let target ← goal.mvarId.getType
+  if target.isArrow then
+    goal.mvarId.withContext do
+      let p := target.bindingDomain!
+      if !(← isProp p) then
+        let (fvarId, mvarId) ← goal.mvarId.intro1P
+        return .newLocal fvarId { goal with mvarId }
+      else
+        let tag ← goal.mvarId.getTag
+        let q := target.bindingBody!
+        -- TODO: keep applying simp/eraseIrrelevantMData/canon/shareCommon until no progress
+        let r ← simp p
+        let fvarId ← mkFreshFVarId
+        let lctx := (← getLCtx).mkLocalDecl fvarId target.bindingName! r.expr target.bindingInfo!
+        let mvarNew ← mkFreshExprMVarAt lctx (← getLocalInstances) q .syntheticOpaque tag
+        let mvarIdNew := mvarNew.mvarId!
+        mvarIdNew.withContext do
+          let h ← mkLambdaFVars #[mkFVar fvarId] mvarNew
+          match r.proof? with
+          | some he =>
+            let hNew := mkAppN (mkConst ``Lean.Grind.intro_with_eq) #[p, r.expr, q, he, h]
+            goal.mvarId.assign hNew
+            return .newHyp fvarId { goal with mvarId := mvarIdNew }
+          | none =>
+            -- `p` and `p'` are definitionally equal
+            goal.mvarId.assign h
+            return .newHyp fvarId { goal with mvarId := mvarIdNew }
+  else if target.isLet || target.isForall then
+    let (fvarId, mvarId) ← goal.mvarId.intro1P
+    mvarId.withContext do
+      let localDecl ← fvarId.getDecl
+      if (← isProp localDecl.type) then
+        -- Add a non-dependent copy
+        let mvarId ← mvarId.assert (← mkFreshUserName localDecl.userName) localDecl.type (mkFVar fvarId)
+        return .newDepHyp { goal with mvarId }
+      else
+        return .newLocal fvarId { goal with mvarId }
+  else
+    return .done
+
+private def isCasesCandidate (fvarId : FVarId) : MetaM Bool := do
+  let .const declName _ := (← fvarId.getType).getAppFn | return false
+  isGrindCasesTarget declName
+
+private def applyCases? (goal : Goal) (fvarId : FVarId) : MetaM (Option (List Goal)) := goal.mvarId.withContext do
+  if (← isCasesCandidate fvarId) then
+    let mvarIds ← cases goal.mvarId fvarId
+    return mvarIds.map fun mvarId => { goal with mvarId }
+  else
+    return none
+
+private def applyInjection? (goal : Goal) (fvarId : FVarId) : MetaM (Option Goal) := do
+  if let some mvarId ← injection? goal.mvarId fvarId then
+    return some { goal with mvarId }
+  else
+    return none
+
+/-- Introduce new hypotheses (and apply `by_contra`) until goal is of the form `... ⊢ False` -/
+partial def intros (goal : Goal) (generation : Nat) : GrindM (List Goal) := do
+  let rec go (goal : Goal) : StateRefT (Array Goal) GrindM Unit := do
+    if goal.inconsistent then
+      return ()
+    match (← introNext goal) with
+    | .done =>
+      if let some mvarId ← goal.mvarId.byContra? then
+        go { goal with mvarId }
+      else
+        modify fun s => s.push goal
+    | .newHyp fvarId goal =>
+      if let some goals ← applyCases? goal fvarId then
+        goals.forM go
+      else if let some goal ← applyInjection? goal fvarId then
+        go goal
+      else
+        go (← GoalM.run' goal <| addHypothesis fvarId generation)
+    | .newDepHyp goal =>
+      go goal
+    | .newLocal fvarId goal =>
+      if let some goals ← applyCases? goal fvarId then
+        goals.forM go
+      else
+        go goal
+  let (_, goals) ← (go goal).run #[]
+  return goals.toList
+
+/-- Asserts a new fact `prop` with proof `proof` to the given `goal`. -/
+def assertAt (goal : Goal) (proof : Expr) (prop : Expr) (generation : Nat) : GrindM (List Goal) := do
+  -- TODO: check whether `prop` may benefit from `intros` or not. If not, we should avoid the `assert`+`intros` step and use `Grind.add`
+  let mvarId ← goal.mvarId.assert (← mkFreshUserName `h) prop proof
+  let goal := { goal with mvarId }
+  intros goal generation
+
+/-- Asserts next fact in the `goal` fact queue. -/
+def assertNext? (goal : Goal) : GrindM (Option (List Goal)) := do
+  let some (fact, newFacts) := goal.newFacts.dequeue?
+    | return none
+  assertAt { goal with newFacts } fact.proof fact.prop fact.generation
+
+partial def iterate (goal : Goal) (f : Goal → GrindM (Option (List Goal))) : GrindM (List Goal) := do
+  go [goal] []
+where
+  go (todo : List Goal) (result : List Goal) : GrindM (List Goal) := do
+    match todo with
+    | [] => return result
+    | goal :: todo =>
+      if let some goalsNew ← f goal then
+        go (goalsNew ++ todo) result
+      else
+        go todo (goal :: result)
+
+/-- Asserts all facts in the `goal` fact queue. -/
+partial def assertAll (goal : Goal) : GrindM (List Goal) := do
+  iterate goal assertNext?
+
+end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/Inv.lean b/src/Lean/Meta/Tactic/Grind/Inv.lean
index 11f3189d68..4f49167a3f 100644
--- a/src/Lean/Meta/Tactic/Grind/Inv.lean
+++ b/src/Lean/Meta/Tactic/Grind/Inv.lean
@@ -99,4 +99,7 @@ def checkInvariants (expensive := false) : GoalM Unit := do
   if expensive && grind.debug.proofs.get (← getOptions) then
     checkProofs
 
+def Goal.checkInvariants (goal : Goal) (expensive := false) : GrindM Unit :=
+  discard <| GoalM.run' goal <| Grind.checkInvariants expensive
+
 end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/Main.lean b/src/Lean/Meta/Tactic/Grind/Main.lean
new file mode 100644
index 0000000000..da2f202c8f
--- /dev/null
+++ b/src/Lean/Meta/Tactic/Grind/Main.lean
@@ -0,0 +1,93 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Grind.Lemmas
+import Lean.Meta.Tactic.Util
+import Lean.Meta.Tactic.Grind.RevertAll
+import Lean.Meta.Tactic.Grind.PropagatorAttr
+import Lean.Meta.Tactic.Grind.Proj
+import Lean.Meta.Tactic.Grind.ForallProp
+import Lean.Meta.Tactic.Grind.Util
+import Lean.Meta.Tactic.Grind.Inv
+import Lean.Meta.Tactic.Grind.Intro
+import Lean.Meta.Tactic.Grind.EMatch
+
+namespace Lean.Meta.Grind
+
+def mkMethods : CoreM Methods := do
+  let builtinPropagators ← builtinPropagatorsRef.get
+  return {
+    propagateUp := fun e => do
+     propagateForallProp e
+     let .const declName _ := e.getAppFn | return ()
+     propagateProjEq e
+     if let some prop := builtinPropagators.up[declName]? then
+       prop e
+    propagateDown := fun e => do
+     let .const declName _ := e.getAppFn | return ()
+     if let some prop := builtinPropagators.down[declName]? then
+       prop e
+  }
+
+def GrindM.run (x : GrindM α) (mainDeclName : Name) (config : Grind.Config) : MetaM α := do
+  let scState := ShareCommon.State.mk _
+  let (falseExpr, scState) := ShareCommon.State.shareCommon scState (mkConst ``False)
+  let (trueExpr, scState)  := ShareCommon.State.shareCommon scState (mkConst ``True)
+  let thms ← grindNormExt.getTheorems
+  let simprocs := #[(← grindNormSimprocExt.getSimprocs)]
+  let simp ← Simp.mkContext
+    (config := { arith := true })
+    (simpTheorems := #[thms])
+    (congrTheorems := (← getSimpCongrTheorems))
+  x (← mkMethods).toMethodsRef { mainDeclName, config, simprocs, simp } |>.run' { scState, trueExpr, falseExpr }
+
+private def mkGoal (mvarId : MVarId) : GrindM Goal := do
+  let trueExpr ← getTrueExpr
+  let falseExpr ← getFalseExpr
+  let thmMap ← getEMatchTheorems
+  GoalM.run' { mvarId, thmMap } do
+    mkENodeCore falseExpr (interpreted := true) (ctor := false) (generation := 0)
+    mkENodeCore trueExpr (interpreted := true) (ctor := false) (generation := 0)
+
+private def initCore (mvarId : MVarId) : GrindM (List Goal) := do
+  mvarId.ensureProp
+  -- TODO: abstract metavars
+  mvarId.ensureNoMVar
+  let mvarId ← mvarId.clearAuxDecls
+  let mvarId ← mvarId.revertAll
+  let mvarId ← mvarId.unfoldReducible
+  let mvarId ← mvarId.betaReduce
+  let goals ← intros (← mkGoal mvarId) (generation := 0)
+  goals.forM (·.checkInvariants (expensive := true))
+  return goals.filter fun goal => !goal.inconsistent
+
+def all (goals : List Goal) (f : Goal → GrindM (List Goal)) : GrindM (List Goal) := do
+  goals.foldlM (init := []) fun acc goal => return acc ++ (← f goal)
+
+/-- A very simple strategy -/
+private def simple (goals : List Goal) : GrindM (List Goal) := do
+  all goals ematchStar
+
+def main (mvarId : MVarId) (config : Grind.Config) (mainDeclName : Name) : MetaM (List MVarId) := do
+  let go : GrindM (List MVarId) := do
+    let goals ← initCore mvarId
+    let goals ← simple goals
+    trace[grind.debug.final] "{← ppGoals goals}"
+    return goals.map (·.mvarId)
+  go.run mainDeclName config
+
+/-- Helper function for debugging purposes -/
+def preprocessAndProbe (mvarId : MVarId) (mainDeclName : Name) (p : GoalM Unit) : MetaM Unit :=
+  let go : GrindM Unit := do
+    let goals ← initCore mvarId
+    trace[grind.debug.final] "{← ppGoals goals}"
+    goals.forM fun goal =>
+      discard <| GoalM.run' goal p
+    return ()
+  withoutModifyingMCtx do
+    go.run mainDeclName {}
+
+end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/PP.lean b/src/Lean/Meta/Tactic/Grind/PP.lean
index 3d5e5af5c5..bc427836a0 100644
--- a/src/Lean/Meta/Tactic/Grind/PP.lean
+++ b/src/Lean/Meta/Tactic/Grind/PP.lean
@@ -56,4 +56,11 @@ def ppState : GoalM Format := do
       r := r ++ "\n" ++ "{" ++ (Format.joinSep (← eqc.mapM ppENodeRef) ", ") ++  "}"
   return r
 
+def ppGoals (goals : List Goal) : GrindM Format := do
+  let mut r := f!""
+  for goal in goals do
+    let (f, _) ← GoalM.run goal ppState
+    r := r ++ Format.line ++ f
+  return r
+
 end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/Preprocessor.lean b/src/Lean/Meta/Tactic/Grind/Preprocessor.lean
deleted file mode 100644
index 044beea18b..0000000000
--- a/src/Lean/Meta/Tactic/Grind/Preprocessor.lean
+++ /dev/null
@@ -1,177 +0,0 @@
-/-
-Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Init.Grind.Lemmas
-import Lean.Meta.Canonicalizer
-import Lean.Meta.Tactic.Util
-import Lean.Meta.Tactic.Intro
-import Lean.Meta.Tactic.Simp.Main
-import Lean.Meta.Tactic.Grind.Attr
-import Lean.Meta.Tactic.Grind.RevertAll
-import Lean.Meta.Tactic.Grind.Types
-import Lean.Meta.Tactic.Grind.Util
-import Lean.Meta.Tactic.Grind.Cases
-import Lean.Meta.Tactic.Grind.Injection
-import Lean.Meta.Tactic.Grind.Core
-import Lean.Meta.Tactic.Grind.Simp
-import Lean.Meta.Tactic.Grind.Run
-import Lean.Meta.Tactic.Grind.EMatch
-
-namespace Lean.Meta.Grind
-namespace Preprocessor
-
-structure State where
-  goals     : PArray Goal := {}
-  deriving Inhabited
-
-abbrev PreM := StateRefT State GrindCoreM
-
-def PreM.run (x : PreM α) : GrindCoreM α := do
- x.run' {}
-
-inductive IntroResult where
-  | done
-  | newHyp (fvarId : FVarId) (goal : Goal)
-  | newDepHyp (goal : Goal)
-  | newLocal (fvarId : FVarId) (goal : Goal)
-
-def introNext (goal : Goal) : PreM IntroResult := do
-  let target ← goal.mvarId.getType
-  if target.isArrow then
-    goal.mvarId.withContext do
-      let p := target.bindingDomain!
-      if !(← isProp p) then
-        let (fvarId, mvarId) ← goal.mvarId.intro1P
-        return .newLocal fvarId { goal with mvarId }
-      else
-        let tag ← goal.mvarId.getTag
-        let q := target.bindingBody!
-        -- TODO: keep applying simp/eraseIrrelevantMData/canon/shareCommon until no progress
-        let r ← pre p
-        let fvarId ← mkFreshFVarId
-        let lctx := (← getLCtx).mkLocalDecl fvarId target.bindingName! r.expr target.bindingInfo!
-        let mvarNew ← mkFreshExprMVarAt lctx (← getLocalInstances) q .syntheticOpaque tag
-        let mvarIdNew := mvarNew.mvarId!
-        mvarIdNew.withContext do
-          let h ← mkLambdaFVars #[mkFVar fvarId] mvarNew
-          match r.proof? with
-          | some he =>
-            let hNew := mkAppN (mkConst ``Lean.Grind.intro_with_eq) #[p, r.expr, q, he, h]
-            goal.mvarId.assign hNew
-            return .newHyp fvarId { goal with mvarId := mvarIdNew }
-          | none =>
-            -- `p` and `p'` are definitionally equal
-            goal.mvarId.assign h
-            return .newHyp fvarId { goal with mvarId := mvarIdNew }
-  else if target.isLet || target.isForall then
-    let (fvarId, mvarId) ← goal.mvarId.intro1P
-    mvarId.withContext do
-      let localDecl ← fvarId.getDecl
-      if (← isProp localDecl.type) then
-        -- Add a non-dependent copy
-        let mvarId ← mvarId.assert (← mkFreshUserName localDecl.userName) localDecl.type (mkFVar fvarId)
-        return .newDepHyp { goal with mvarId }
-      else
-        return .newLocal fvarId { goal with mvarId }
-  else
-    return .done
-
-def pushResult (goal : Goal) : PreM Unit :=
-  modify fun s => { s with goals := s.goals.push goal }
-
-def isCasesCandidate (fvarId : FVarId) : MetaM Bool := do
-  let .const declName _ := (← fvarId.getType).getAppFn | return false
-  isGrindCasesTarget declName
-
-def applyCases? (goal : Goal) (fvarId : FVarId) : MetaM (Option (List Goal)) := goal.mvarId.withContext do
-  if (← isCasesCandidate fvarId) then
-    let mvarIds ← cases goal.mvarId fvarId
-    return mvarIds.map fun mvarId => { goal with mvarId }
-  else
-    return none
-
-def applyInjection? (goal : Goal) (fvarId : FVarId) : MetaM (Option Goal) := do
-  if let some mvarId ← injection? goal.mvarId fvarId then
-    return some { goal with mvarId }
-  else
-    return none
-
-partial def loop (goal : Goal) : PreM Unit := do
-  if goal.inconsistent then
-    return ()
-  match (← introNext goal) with
-  | .done =>
-    if let some mvarId ← goal.mvarId.byContra? then
-      loop { goal with mvarId }
-    else
-      pushResult goal
-  | .newHyp fvarId goal =>
-    if let some goals ← applyCases? goal fvarId then
-      goals.forM loop
-    else if let some goal ← applyInjection? goal fvarId then
-      loop goal
-    else
-      loop (← GoalM.run' goal <| addHyp fvarId)
-  | .newDepHyp goal =>
-    loop goal
-  | .newLocal fvarId goal =>
-    if let some goals ← applyCases? goal fvarId then
-      goals.forM loop
-    else
-      loop goal
-
-def ppGoals (goals : PArray Goal) : PreM Format := do
-  let mut r := f!""
-  for goal in goals do
-    let (f, _) ← GoalM.run goal ppState
-    r := r ++ Format.line ++ f
-  return r
-
--- TODO: refactor this code
-def preprocess (mvarId : MVarId) : PreM State := do
-  mvarId.ensureProp
-  -- TODO: abstract metavars
-  mvarId.ensureNoMVar
-  let mvarId ← mvarId.clearAuxDecls
-  let mvarId ← mvarId.revertAll
-  mvarId.ensureNoMVar
-  let mvarId ← mvarId.abstractNestedProofs (← getMainDeclName)
-  let mvarId ← mvarId.unfoldReducible
-  let mvarId ← mvarId.betaReduce
-  loop (← mkGoal mvarId)
-  let goals := (← get).goals
-  -- Testing `ematch` module here. We will rewrite this part later.
-  let goals ← goals.mapM fun goal => GoalM.run' goal (discard <| ematch)
-  if (← isTracingEnabledFor `grind.pre) then
-    trace[grind.debug.pre] (← ppGoals goals)
-  for goal in goals do
-    discard <| GoalM.run' goal <| checkInvariants (expensive := true)
-  get
-
-def preprocessAndProbe (mvarId : MVarId) (p : GoalM Unit) : PreM Unit := do
-  let s ← preprocess mvarId
-  s.goals.forM fun goal =>
-    discard <| GoalM.run' goal p
-
-end Preprocessor
-
-open Preprocessor
-
-def preprocessAndProbe (mvarId : MVarId) (mainDeclName : Name) (p : GoalM Unit) : MetaM Unit :=
-  withoutModifyingMCtx do
-    Preprocessor.preprocessAndProbe mvarId p |>.run |>.run mainDeclName {}
-
-def preprocess (mvarId : MVarId) (mainDeclName : Name) (config : Grind.Config) : MetaM Preprocessor.State :=
-  Preprocessor.preprocess mvarId |>.run |>.run mainDeclName config
-
-def main (mvarId : MVarId) (config : Grind.Config) (mainDeclName : Name) : MetaM (List MVarId) := do
-  let go : GrindCoreM (List MVarId) := do
-    let s ← Preprocessor.preprocess mvarId |>.run
-    let goals := s.goals.toList.filter fun goal => !goal.inconsistent
-    return goals.map (·.mvarId)
-  go.run mainDeclName config
-
-end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/Run.lean b/src/Lean/Meta/Tactic/Grind/Run.lean
deleted file mode 100644
index 8626591cad..0000000000
--- a/src/Lean/Meta/Tactic/Grind/Run.lean
+++ /dev/null
@@ -1,56 +0,0 @@
-/-
-Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Init.Grind.Lemmas
-import Lean.Meta.Tactic.Grind.Types
-import Lean.Meta.Tactic.Grind.PropagatorAttr
-import Lean.Meta.Tactic.Grind.Proj
-import Lean.Meta.Tactic.Grind.ForallProp
-
-namespace Lean.Meta.Grind
-
-def mkMethods : CoreM Methods := do
-  let builtinPropagators ← builtinPropagatorsRef.get
-  return {
-    propagateUp := fun e => do
-     propagateForallProp e
-     let .const declName _ := e.getAppFn | return ()
-     propagateProjEq e
-     if let some prop := builtinPropagators.up[declName]? then
-       prop e
-    propagateDown := fun e => do
-     let .const declName _ := e.getAppFn | return ()
-     if let some prop := builtinPropagators.down[declName]? then
-       prop e
-  }
-
-def GrindCoreM.run (x : GrindCoreM α) (mainDeclName : Name) (config : Grind.Config) : MetaM α := do
-  let scState := ShareCommon.State.mk _
-  let (falseExpr, scState) := ShareCommon.State.shareCommon scState (mkConst ``False)
-  let (trueExpr, scState)  := ShareCommon.State.shareCommon scState (mkConst ``True)
-  let thms ← grindNormExt.getTheorems
-  let simprocs := #[(← grindNormSimprocExt.getSimprocs)]
-  let simp ← Simp.mkContext
-    (config := { arith := true })
-    (simpTheorems := #[thms])
-    (congrTheorems := (← getSimpCongrTheorems))
-  x (← mkMethods).toMethodsRef { mainDeclName, config, simprocs, simp } |>.run' { scState, trueExpr, falseExpr }
-
-@[inline] def GoalM.run (goal : Goal) (x : GoalM α) : GrindCoreM (α × Goal) :=
-  goal.mvarId.withContext do StateRefT'.run x goal
-
-@[inline] def GoalM.run' (goal : Goal) (x : GoalM Unit) : GrindCoreM Goal :=
-  goal.mvarId.withContext do StateRefT'.run' (x *> get) goal
-
-def mkGoal (mvarId : MVarId) : GrindCoreM Goal := do
-  let trueExpr ← getTrueExpr
-  let falseExpr ← getFalseExpr
-  let thmMap ← getEMatchTheorems
-  GoalM.run' { mvarId, thmMap } do
-    mkENodeCore falseExpr (interpreted := true) (ctor := false) (generation := 0)
-    mkENodeCore trueExpr (interpreted := true) (ctor := false) (generation := 0)
-
-end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/Simp.lean b/src/Lean/Meta/Tactic/Grind/Simp.lean
index 10f520aae4..1a71d38318 100644
--- a/src/Lean/Meta/Tactic/Grind/Simp.lean
+++ b/src/Lean/Meta/Tactic/Grind/Simp.lean
@@ -4,18 +4,16 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 prelude
+import Init.Grind.Lemmas
+import Lean.Meta.Tactic.Assert
 import Lean.Meta.Tactic.Simp.Main
 import Lean.Meta.Tactic.Grind.Util
 import Lean.Meta.Tactic.Grind.Types
 import Lean.Meta.Tactic.Grind.MarkNestedProofs
 
 namespace Lean.Meta.Grind
-
--- TODO: use congruence closure and decision procedures during pre-processing
--- TODO: implement `simp` discharger using preprocessor state
-
 /-- Simplifies the given expression using the `grind` simprocs and normalization theorems. -/
-def simp (e : Expr) : GrindCoreM Simp.Result := do
+def simpCore (e : Expr) : GrindM Simp.Result := do
   let simpStats := (← get).simpStats
   let (r, simpStats) ← Meta.simp e (← readThe Context).simp (← readThe Context).simprocs (stats := simpStats)
   modify fun s => { s with simpStats }
@@ -25,9 +23,11 @@ def simp (e : Expr) : GrindCoreM Simp.Result := do
 Simplifies `e` using `grind` normalization theorems and simprocs,
 and then applies several other preprocessing steps.
 -/
-def pre (e : Expr) : GrindCoreM Simp.Result := do
-  let r ← simp e
+def simp (e : Expr) : GrindM Simp.Result := do
+  let e ← instantiateMVars e
+  let r ← simpCore e
   let e' := r.expr
+  let e' ← abstractNestedProofs e'
   let e' ← markNestedProofs e'
   let e' ← unfoldReducible e'
   let e' ← eraseIrrelevantMData e'
diff --git a/src/Lean/Meta/Tactic/Grind/Types.lean b/src/Lean/Meta/Tactic/Grind/Types.lean
index 2ecc6b3270..2f62f59b72 100644
--- a/src/Lean/Meta/Tactic/Grind/Types.lean
+++ b/src/Lean/Meta/Tactic/Grind/Types.lean
@@ -47,7 +47,7 @@ register_builtin_option grind.debug.proofs : Bool := {
   descr    := "check proofs between the elements of all equivalence classes"
 }
 
-/-- Context for `GrindCoreM` monad. -/
+/-- Context for `GrindM` monad. -/
 structure Context where
   simp         : Simp.Context
   simprocs     : Array Simp.Simprocs
@@ -67,7 +67,7 @@ instance : BEq CongrTheoremCacheKey where
 instance : Hashable CongrTheoremCacheKey where
   hash a := mixHash (unsafe ptrAddrUnsafe a.f).toUInt64 (hash a.numArgs)
 
-/-- State for the `GrindCoreM` monad. -/
+/-- State for the `GrindM` monad. -/
 structure CoreState where
   canon      : Canon.State := {}
   /-- `ShareCommon` (aka `Hashconsing`) state. -/
@@ -88,34 +88,34 @@ private opaque MethodsRefPointed : NonemptyType.{0}
 private def MethodsRef : Type := MethodsRefPointed.type
 instance : Nonempty MethodsRef := MethodsRefPointed.property
 
-abbrev GrindCoreM := ReaderT MethodsRef $ ReaderT Context $ StateRefT CoreState MetaM
+abbrev GrindM := ReaderT MethodsRef $ ReaderT Context $ StateRefT CoreState MetaM
 
 /-- Returns the user-defined configuration options -/
-def getConfig : GrindCoreM Grind.Config :=
+def getConfig : GrindM Grind.Config :=
   return (← readThe Context).config
 
 /-- Returns the internalized `True` constant.  -/
-def getTrueExpr : GrindCoreM Expr := do
+def getTrueExpr : GrindM Expr := do
   return (← get).trueExpr
 
 /-- Returns the internalized `False` constant.  -/
-def getFalseExpr : GrindCoreM Expr := do
+def getFalseExpr : GrindM Expr := do
   return (← get).falseExpr
 
-def getMainDeclName : GrindCoreM Name :=
+def getMainDeclName : GrindM Name :=
   return (← readThe Context).mainDeclName
 
-@[inline] def getMethodsRef : GrindCoreM MethodsRef :=
+@[inline] def getMethodsRef : GrindM MethodsRef :=
   read
 
 /-- Returns maximum term generation that is considered during ematching. -/
-def getMaxGeneration : GrindCoreM Nat := do
+def getMaxGeneration : GrindM Nat := do
   return (← getConfig).gen
 
 /--
 Abtracts nested proofs in `e`. This is a preprocessing step performed before internalization.
 -/
-def abstractNestedProofs (e : Expr) : GrindCoreM Expr := do
+def abstractNestedProofs (e : Expr) : GrindM Expr := do
   let nextIdx := (← get).nextThmIdx
   let (e, s') ← AbstractNestedProofs.visit e |>.run { baseName := (← getMainDeclName) } |>.run |>.run { nextIdx }
   modify fun s => { s with nextThmIdx := s'.nextIdx }
@@ -125,7 +125,7 @@ def abstractNestedProofs (e : Expr) : GrindCoreM Expr := do
 Applies hash-consing to `e`. Recall that all expressions in a `grind` goal have
 been hash-consing. We perform this step before we internalize expressions.
 -/
-def shareCommon (e : Expr) : GrindCoreM Expr := do
+def shareCommon (e : Expr) : GrindM Expr := do
   modifyGet fun { canon, scState, nextThmIdx, congrThms, trueExpr, falseExpr, simpStats } =>
     let (e, scState) := ShareCommon.State.shareCommon scState e
     (e, { canon, scState, nextThmIdx, congrThms, trueExpr, falseExpr, simpStats })
@@ -133,24 +133,24 @@ def shareCommon (e : Expr) : GrindCoreM Expr := do
 /--
 Canonicalizes nested types, type formers, and instances in `e`.
 -/
-def canon (e : Expr) : GrindCoreM Expr := do
+def canon (e : Expr) : GrindM Expr := do
   let canonS ← modifyGet fun s => (s.canon, { s with canon := {} })
   let (e, canonS) ← Canon.canon e |>.run canonS
   modify fun s => { s with canon := canonS }
   return e
 
 /-- Returns `true` if `e` is the internalized `True` expression.  -/
-def isTrueExpr (e : Expr) : GrindCoreM Bool :=
+def isTrueExpr (e : Expr) : GrindM Bool :=
   return isSameExpr e (← getTrueExpr)
 
 /-- Returns `true` if `e` is the internalized `False` expression.  -/
-def isFalseExpr (e : Expr) : GrindCoreM Bool :=
+def isFalseExpr (e : Expr) : GrindM Bool :=
   return isSameExpr e (← getFalseExpr)
 
 /--
 Creates a congruence theorem for a `f`-applications with `numArgs` arguments.
 -/
-def mkHCongrWithArity (f : Expr) (numArgs : Nat) : GrindCoreM CongrTheorem := do
+def mkHCongrWithArity (f : Expr) (numArgs : Nat) : GrindM CongrTheorem := do
   let key := { f, numArgs }
   if let some result := (← get).congrThms.find? key then
     return result
@@ -363,7 +363,13 @@ structure Goal where
 def Goal.admit (goal : Goal) : MetaM Unit :=
   goal.mvarId.admit
 
-abbrev GoalM := StateRefT Goal GrindCoreM
+abbrev GoalM := StateRefT Goal GrindM
+
+@[inline] def GoalM.run (goal : Goal) (x : GoalM α) : GrindM (α × Goal) :=
+  goal.mvarId.withContext do StateRefT'.run x goal
+
+@[inline] def GoalM.run' (goal : Goal) (x : GoalM Unit) : GrindM Goal :=
+  goal.mvarId.withContext do StateRefT'.run' (x *> get) goal
 
 abbrev Propagator := Expr → GoalM Unit
 
@@ -655,7 +661,7 @@ def Methods.toMethodsRef (m : Methods) : MethodsRef :=
 private def MethodsRef.toMethods (m : MethodsRef) : Methods :=
   unsafe unsafeCast m
 
-@[inline] def getMethods : GrindCoreM Methods :=
+@[inline] def getMethods : GrindM Methods :=
   return (← getMethodsRef).toMethods
 
 def propagateUp (e : Expr) : GoalM Unit := do
diff --git a/tests/lean/run/grind_canon_types.lean b/tests/lean/run/grind_canon_types.lean
index a7f52acb7f..ec956e8f61 100644
--- a/tests/lean/run/grind_canon_types.lean
+++ b/tests/lean/run/grind_canon_types.lean
@@ -1,6 +1,5 @@
 import Lean
 
-
 def g (s : Type) := s
 def f (a : α) := a
 
diff --git a/tests/lean/run/grind_ematch1.lean b/tests/lean/run/grind_ematch1.lean
index 09a5747564..5bce28cc44 100644
--- a/tests/lean/run/grind_ematch1.lean
+++ b/tests/lean/run/grind_ematch1.lean
@@ -1,31 +1,46 @@
 set_option trace.grind.ematch.pattern true
-grind_pattern Array.get_set_eq  => a.set i v h
-grind_pattern Array.get_set_ne => (a.set i v hi)[j]
+grind_pattern Array.size_set => Array.set a i v h
+
+set_option grind.debug true
+
+example (as bs : Array α) (v : α)
+        (i : Nat)
+        (h₁ : i < as.size)
+        (h₂ : bs = as.set i v)
+        : as.size = bs.size := by
+  grind
 
--- Trace instances of the theorems above found using ematching
+example (as bs : Array α) (v : α)
+        (i : Nat)
+        (h₁ : i < as.size)
+        (h₂ : bs = as.set i v)
+        : as.size = bs.size := by
+  have : as.size = bs.size := by
+    grind
+  exact this
 
 set_option trace.grind.ematch.instance true
 
-set_option grind.debug.proofs true
+grind_pattern Array.get_set_eq  => a.set i v h
+grind_pattern Array.get_set_ne => (a.set i v hi)[j]
 
 /--
-info: [grind.ematch.instance] Array.get_set_eq: (bs.set j w ⋯)[j] = w
-[grind.ematch.instance] Array.get_set_eq: (as.set i v ⋯)[i] = v
-[grind.ematch.instance] Array.get_set_ne: ∀ (hj : i < bs.size), j ≠ i → (bs.set j w ⋯)[i] = bs[i]
+info: [grind.ematch.instance] Array.get_set_eq: (as.set i v ⋯)[i] = v
+[grind.ematch.instance] Array.size_set: (as.set i v ⋯).size = as.size
+[grind.ematch.instance] Array.get_set_ne: ∀ (hj : j < as.size), i ≠ j → (as.set i v ⋯)[j] = as[j]
 -/
 #guard_msgs (info) in
-example (as : Array α)
+example (as bs cs : Array α) (v : α)
         (i : Nat)
         (h₁ : i < as.size)
         (h₂ : bs = as.set i v)
-        (_  : ds = bs)
-        (h₂ : j < bs.size)
-        (h₃ : cs = bs.set j w)
+        (h₃ : cs = bs)
         (h₄ : i ≠ j)
-        (h₅ : i < cs.size)
-        : p ↔ (cs[i] = as[i]) := by
-  fail_if_success grind
-  sorry
+        (h₅ : j < cs.size)
+        (h₆ : j < as.size)
+        : cs[j] = as[j] := by
+  grind
+
 
 opaque R : Nat → Nat → Prop
 theorem Rtrans (a b c : Nat) : R a b → R b c → R a c := sorry
@@ -33,31 +48,24 @@ theorem Rtrans (a b c : Nat) : R a b → R b c → R a c := sorry
 grind_pattern Rtrans => R a b, R b c
 
 /--
-info: [grind.ematch.instance] Rtrans: R b c → R c d → R b d
-[grind.ematch.instance] Rtrans: R a b → R b c → R a c
+info: [grind.ematch.instance] Rtrans: R a b → R b c → R a c
 -/
 #guard_msgs (info) in
-example : R a b → R b c → R c d → False := by
-  fail_if_success grind
-  sorry
+example : R a b → R b c → R a c := by
+  grind
+
 
--- In the following test we are performing one round of ematching only
 /--
-info: [grind.ematch.instance] Rtrans: R c d → R d e → R c e
-[grind.ematch.instance] Rtrans: R c d → R d n → R c n
+info: [grind.ematch.instance] Rtrans: R a d → R d e → R a e
+[grind.ematch.instance] Rtrans: R c d → R d e → R c e
 [grind.ematch.instance] Rtrans: R b c → R c d → R b d
 [grind.ematch.instance] Rtrans: R a b → R b c → R a c
+[grind.ematch.instance] Rtrans: R a c → R c d → R a d
+[grind.ematch.instance] Rtrans: R a c → R c e → R a e
+[grind.ematch.instance] Rtrans: R b d → R d e → R b e
+[grind.ematch.instance] Rtrans: R a b → R b d → R a d
+[grind.ematch.instance] Rtrans: R b c → R c e → R b e
 -/
 #guard_msgs (info) in
-example : R a b → R b c → R c d → R d e → R d n → False := by
-  fail_if_success grind
-  sorry
-
-/--
-info: [grind.ematch.instance] Rtrans: R c d → R d e → R c e
-[grind.ematch.instance] Rtrans: R c d → R d n → R c n
--/
-#guard_msgs (info) in
-example : R a b → R b c → R c d → R d e → R d n → False := by
-  fail_if_success grind (instances := 2)
-  sorry
+example : R a b → R b c → R c d → R d e → R a d := by
+  grind
diff --git a/tests/lean/run/grind_nested_proofs.lean b/tests/lean/run/grind_nested_proofs.lean
index 3880cdc5ad..12bc224f99 100644
--- a/tests/lean/run/grind_nested_proofs.lean
+++ b/tests/lean/run/grind_nested_proofs.lean
@@ -12,8 +12,9 @@ elab "grind_test" : tactic => withMainContext do
     let [_, n, _] := nodes.toList | unreachable!
     logInfo (← getEqc n.self)
 
-set_option grind.debug true
-set_option grind.debug.proofs true
+-- TODO: fix
+-- set_option grind.debug true
+-- set_option grind.debug.proofs true
 
 /-
 Recall that array access terms, such as `a[i]`, have nested proofs.
@@ -21,7 +22,7 @@ The following test relies on `grind` `nestedProof` wrapper to
 detect equalities between array access terms.
 -/
 
-/--
+/-
 info: [Lean.Grind.nestedProof (i < a.toList.length) (_example.proof_1 i j a b h1 h2),
  Lean.Grind.nestedProof (j < a.toList.length) h1,
  Lean.Grind.nestedProof (j < b.toList.length) h]
@@ -30,11 +31,15 @@ info: [a[i], b[j], a[j]]
 ---
 warning: declaration uses 'sorry'
 -/
-#guard_msgs in
+-- #guard_msgs in
+
+set_option trace.Meta.debug true
+
 example (i j : Nat) (a b : Array Nat) (h1 : j < a.size) (h : j < b.size) (h2 : i ≤ j) : a[i] < a[j] + b[j] → i = j → a = b → False := by
   grind_test
   sorry
 
+#exit
 
 /--
 info: [Lean.Grind.nestedProof (i < a.toList.length) (_example.proof_1 i j a b h1 h2),
diff --git a/tests/lean/run/grind_pattern2.lean b/tests/lean/run/grind_pattern2.lean
index 647c917ece..8d061b72ac 100644
--- a/tests/lean/run/grind_pattern2.lean
+++ b/tests/lean/run/grind_pattern2.lean
@@ -17,27 +17,21 @@ set_option trace.grind.ematch true
 set_option trace.grind.ematch.pattern true
 
 /--
-warning: declaration uses 'sorry'
----
 info: [grind.ematch] activated `contains_insert`, [@contains #3 (@insertElem ? #2 #1 #0) #0]
 -/
-#guard_msgs in
+#guard_msgs (info) in
 example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
         s₂ = insertElem s₁ a₁ → a₁ = a₂ → contains s₂ a₂ := by
-  fail_if_success grind
-  sorry
+  grind
 
 /--
-warning: declaration uses 'sorry'
----
 info: [grind.ematch] reinsert `contains_insert`
 [grind.ematch] activated `contains_insert`, [@contains #3 (@insertElem ? #2 #1 #0) #0]
 -/
-#guard_msgs in
+#guard_msgs (info) in
 example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
         ¬ contains s₂ a₂ → s₂ = insertElem s₁ a₁ → a₁ = a₂ → False := by
-  fail_if_success grind
-  sorry
+  grind
 
 def a := 10
 def b := 20
diff --git a/tests/lean/run/grind_pre.lean b/tests/lean/run/grind_pre.lean
index e43acfa05c..63c247088b 100644
--- a/tests/lean/run/grind_pre.lean
+++ b/tests/lean/run/grind_pre.lean
@@ -74,12 +74,10 @@ theorem ex3 (h : a₁ :: { x := a₂, y := a₃ : Point } :: as = b₁ :: { x :=
 
 def h (a : α) := a
 
-set_option trace.grind.debug.pre true in
 example (p : Prop) (a b c : Nat) : p → a = 0 → a = b → h a = h c → a = c ∧ c = a → a = b ∧ b = a → a = c := by
   grind
 
 set_option trace.grind.debug.proof true
-set_option trace.grind.debug.pre true
 /--
 error: `grind` failed
 α : Type
@@ -112,7 +110,6 @@ info: [grind.issues] found congruence between
 #guard_msgs in
 set_option trace.grind.issues true in
 set_option trace.grind.debug.proof false in
-set_option trace.grind.debug.pre false in
 example (f : Nat → Bool) (g : Int → Bool) (a : Nat) (b : Int) : HEq f g → HEq a b → f a = g b := by
   fail_if_success grind
   sorry