diff --git a/src/Init/Grind/Util.lean b/src/Init/Grind/Util.lean
index 34bc7ec2df73..0a58ba5979cc 100644
--- a/src/Init/Grind/Util.lean
+++ b/src/Init/Grind/Util.lean
@@ -31,6 +31,14 @@ When `EqMatch a b origin` is `True`, we mark `origin` as a resolved case-split.
 -/
 def EqMatch (a b : α) {_origin : α} : Prop := a = b
 
+/--
+Gadget for annotating conditions of `match` equational lemmas.
+We use this annotation for two different reasons:
+- We don't want to normalize them.
+- We have a propagator for them.
+-/
+def MatchCond (p : Prop) : Prop := p
+
 theorem nestedProof_congr (p q : Prop) (h : p = q) (hp : p) (hq : q) : HEq (@nestedProof p hp) (@nestedProof q hq) := by
   subst h; apply HEq.refl
 
diff --git a/src/Lean/Meta/Tactic/Grind.lean b/src/Lean/Meta/Tactic/Grind.lean
index 0bb04bafe04c..53f5373b46ba 100644
--- a/src/Lean/Meta/Tactic/Grind.lean
+++ b/src/Lean/Meta/Tactic/Grind.lean
@@ -26,6 +26,8 @@ import Lean.Meta.Tactic.Grind.Main
 import Lean.Meta.Tactic.Grind.CasesMatch
 import Lean.Meta.Tactic.Grind.Arith
 import Lean.Meta.Tactic.Grind.Ext
+import Lean.Meta.Tactic.Grind.MatchCond
+import Lean.Meta.Tactic.Grind.DoNotSimp
 
 namespace Lean
 
@@ -70,5 +72,6 @@ builtin_initialize registerTraceClass `grind.debug.offset
 builtin_initialize registerTraceClass `grind.debug.offset.proof
 builtin_initialize registerTraceClass `grind.debug.ematch.pattern
 builtin_initialize registerTraceClass `grind.debug.beta
+builtin_initialize registerTraceClass `grind.debug.matchCond
 
 end Lean
diff --git a/src/Lean/Meta/Tactic/Grind/EMatch.lean b/src/Lean/Meta/Tactic/Grind/EMatch.lean
index 8341d44add46..bef989aaa6f7 100644
--- a/src/Lean/Meta/Tactic/Grind/EMatch.lean
+++ b/src/Lean/Meta/Tactic/Grind/EMatch.lean
@@ -7,6 +7,7 @@ prelude
 import Lean.Meta.Tactic.Grind.Types
 import Lean.Meta.Tactic.Grind.Intro
 import Lean.Meta.Tactic.Grind.DoNotSimp
+import Lean.Meta.Tactic.Grind.MatchCond
 
 namespace Lean.Meta.Grind
 namespace EMatch
@@ -215,7 +216,11 @@ Helper function for marking parts of `match`-equation theorem as "do-not-simplif
 -/
 private partial def annotateMatchEqnType (prop : Expr) (initApp : Expr) : M Expr := do
   if let .forallE n d b bi := prop then
-    withLocalDecl n bi (← markAsDoNotSimp d) fun x => do
+    let d ← if (← isProp d) then
+      markAsMatchCond d
+    else
+      pure d
+    withLocalDecl n bi d fun x => do
       mkForallFVars #[x] (← annotateMatchEqnType (b.instantiate1 x) initApp)
   else
     let_expr f@Eq α lhs rhs := prop | return prop
diff --git a/src/Lean/Meta/Tactic/Grind/Internalize.lean b/src/Lean/Meta/Tactic/Grind/Internalize.lean
index 8e6c85b1f761..e4ce20405d2f 100644
--- a/src/Lean/Meta/Tactic/Grind/Internalize.lean
+++ b/src/Lean/Meta/Tactic/Grind/Internalize.lean
@@ -110,6 +110,9 @@ private def pushCastHEqs (e : Expr) : GoalM Unit := do
 private def preprocessGroundPattern (e : Expr) : GoalM Expr := do
   shareCommon (← canon (← normalizeLevels (← unfoldReducible e)))
 
+private def mkENode' (e : Expr) (generation : Nat) : GoalM Unit :=
+  mkENodeCore e (ctor := false) (interpreted := false) (generation := generation)
+
 mutual
 /-- Internalizes the nested ground terms in the given pattern. -/
 private partial def internalizePattern (pattern : Expr) (generation : Nat) : GoalM Expr := do
@@ -122,6 +125,24 @@ private partial def internalizePattern (pattern : Expr) (generation : Nat) : Goa
   else pattern.withApp fun f args => do
     return mkAppN f (← args.mapM (internalizePattern · generation))
 
+/-- Internalizes the `MatchCond` gadget. -/
+private partial def internalizeMatchCond (matchCond : Expr) (generation : Nat) : GoalM Unit := do
+  let_expr Grind.MatchCond e ← matchCond | return ()
+  mkENode' matchCond generation
+  let mut e := e
+  repeat
+    let .forallE _ d b _ := e | break
+    let internalizeLhs (lhs : Expr) : GoalM Unit := do
+      unless lhs.hasLooseBVars do
+        internalize lhs generation
+        registerParent matchCond lhs
+    match_expr d with
+    | Eq _ lhs _ => internalizeLhs lhs
+    | HEq _ lhs _ _ => internalizeLhs lhs
+    | _ => pure ()
+    e := b
+  propagateUp matchCond
+
 partial def activateTheorem (thm : EMatchTheorem) (generation : Nat) : GoalM Unit := do
   -- Recall that we use the proof as part of the key for a set of instances found so far.
   -- We don't want to use structural equality when comparing keys.
@@ -164,10 +185,9 @@ partial def internalize (e : Expr) (generation : Nat) (parent? : Option Expr :=
   match e with
   | .bvar .. => unreachable!
   | .sort .. => return ()
-  | .fvar .. | .letE .. | .lam .. =>
-    mkENodeCore e (ctor := false) (interpreted := false) (generation := generation)
+  | .fvar .. | .letE .. | .lam .. => mkENode' e generation
   | .forallE _ d b _ =>
-    mkENodeCore e (ctor := false) (interpreted := false) (generation := generation)
+    mkENode' e generation
     if (← isProp d <&&> isProp e) then
       internalize d generation e
       registerParent e d
@@ -181,12 +201,14 @@ partial def internalize (e : Expr) (generation : Nat) (parent? : Option Expr :=
   | .mdata ..
   | .proj .. =>
     reportIssue m!"unexpected kernel projection term during internalization{indentExpr e}\n`grind` uses a pre-processing step that folds them as projection applications, the pre-processor should have failed to fold this term"
-    mkENodeCore e (ctor := false) (interpreted := false) (generation := generation)
+    mkENode' e generation
   | .app .. =>
     if (← isLitValue e) then
       -- We do not want to internalize the components of a literal value.
       mkENode e generation
       Arith.internalize e parent?
+    else if e.isAppOfArity ``Grind.MatchCond 1 then
+      internalizeMatchCond e generation
     else e.withApp fun f args => do
       checkAndAddSplitCandidate e
       pushCastHEqs e
diff --git a/src/Lean/Meta/Tactic/Grind/MatchCond.lean b/src/Lean/Meta/Tactic/Grind/MatchCond.lean
new file mode 100644
index 000000000000..da3b990c7c9e
--- /dev/null
+++ b/src/Lean/Meta/Tactic/Grind/MatchCond.lean
@@ -0,0 +1,155 @@
+/-
+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
+import Init.Simproc
+import Lean.Meta.Tactic.Simp.Simproc
+import Lean.Meta.Tactic.Grind.PropagatorAttr
+
+namespace Lean.Meta.Grind
+
+/--
+Returns `Grind.MatchCond e`.
+Recall that `Grind.MatchCond` is an identity function,
+but the following simproc is used to prevent the term `e` from being simplified,
+and we have special support for propagating is truth value.
+-/
+def markAsMatchCond (e : Expr) : MetaM Expr :=
+  mkAppM ``Grind.MatchCond #[e]
+
+builtin_dsimproc_decl reduceMatchCond (Grind.MatchCond _) := fun e => do
+  let_expr Grind.MatchCond _ ← e | return .continue
+  return .done e
+
+/-- Adds `reduceMatchCond` to `s` -/
+def addMatchCond (s : Simprocs) : CoreM Simprocs := do
+  s.add ``reduceMatchCond (post := false)
+
+/--
+Helper function for `isSatisfied`.
+See `isSatisfied`.
+-/
+private partial def isMathCondFalseHyp (e : Expr) : GoalM Bool := do
+  match_expr e with
+  | Eq _ lhs rhs => isFalse lhs rhs
+  | HEq _ lhs _ rhs => isFalse lhs rhs
+  | _ => return false
+where
+  isFalse (lhs rhs : Expr) : GoalM Bool := do
+    if lhs.hasLooseBVars then return false
+    let root ← getRootENode lhs
+    if root.ctor then
+      let some ctorLhs ← isConstructorApp? root.self | return false
+      let some ctorRhs ← isConstructorApp? rhs | return false
+      if ctorLhs.name ≠ ctorRhs.name then return true
+      let lhsArgs := root.self.getAppArgs
+      let rhsArgs := rhs.getAppArgs
+      for i in [ctorLhs.numParams : ctorLhs.numParams + ctorLhs.numFields] do
+        if (← isFalse lhsArgs[i]! rhsArgs[i]!) then
+          return true
+      return false
+    else if root.interpreted then
+      if rhs.hasLooseBVars then return false
+      unless (← isLitValue rhs) do return false
+      return (← normLitValue root.self) != (← normLitValue rhs)
+    else
+      return false
+
+/--
+Returns `true` if `e` is a `Grind.MatchCond`, and it has been satifisfied.
+Recall that we use `Grind.MatchCond` to annotate conditional `match`-equations.
+Consider the following example:
+```
+inductive S where
+  | mk1 (n : Nat)
+  | mk2 (n : Nat) (s : S)
+  | mk3 (n : Bool)
+  | mk4 (s1 s2 : S)
+
+def f (x y : S) :=
+  match x, y with
+  | .mk1 _, _ => 2
+  | _, .mk2 1 (.mk4 _ _) => 3
+  | .mk3 _, _ => 4
+  | _, _ => 5
+```
+The `match`-expression in the example above has overlapping patterns and
+consequently produces conditional `match` equations. Thus, `grind` generates
+the following auxiliary `Grind.MatchCond` terms for an application `f a b`:
+- `Grind.MatchCond (∀ (n : Nat), a = S.mk1 n → False)`
+- `Grind.MatchCond (∀ (s1 s2 : S), b = S.mk2 1 (s1.mk4 s2) → False)`
+- `Grind.MatchCond (∀ (n : Bool), a = S.mk3 n → False)`
+
+`isSatisfied` uses the fact that constructor applications and literal values
+are always the root of their equivalence classes.
+-/
+private partial def isStatisfied (e : Expr) : GoalM Bool := do
+  let_expr Grind.MatchCond e ← e | return false
+  let mut e := e
+  repeat
+    let .forallE _ d b _ := e | break
+    if (← isMathCondFalseHyp d) then
+      trace[grind.debug.matchCond] "satifised{indentExpr e}\nthe following equality is false{indentExpr d}"
+      return true
+    e := b
+  return false
+
+private partial def mkMathCondProof? (e : Expr) : GoalM (Option Expr) := do
+  let_expr Grind.MatchCond f ← e | return none
+  forallTelescopeReducing f fun xs _ => do
+    for x in xs do
+      let type ← inferType x
+      if (← isMathCondFalseHyp type) then
+        trace[grind.debug.matchCond] ">>> {type}"
+        let some h ← go? x | pure ()
+        return some (← mkLambdaFVars xs h)
+    return none
+where
+  go? (h : Expr) : GoalM (Option Expr) := do
+    trace[grind.debug.matchCond] "go?: {← inferType h}"
+    let (lhs, rhs, isHeq) ← match_expr (← inferType h) with
+      | Eq _ lhs rhs => pure (lhs, rhs, false)
+      | HEq _ lhs _ rhs => pure (lhs, rhs, true)
+      | _ => return none
+    let target ← (← get).mvarId.getType
+    let root ← getRootENode lhs
+    let h ← if isHeq then
+      mkEqOfHEq (← mkHEqTrans (← mkHEqProof root.self lhs) h)
+    else
+      mkEqTrans (← mkEqProof root.self lhs) h
+    if root.ctor then
+      let some ctorLhs ← isConstructorApp? root.self | return none
+      let some ctorRhs ← isConstructorApp? rhs | return none
+      let h ← mkNoConfusion target h
+      if ctorLhs.name ≠ ctorRhs.name then
+        return some h
+      else
+        let .forallE _ k _ _ ← whnfD (← inferType h)
+          | return none
+        forallTelescopeReducing k fun xs _ => do
+          for x in xs do
+            let some hx ← go? x | pure ()
+            return some (mkApp h (← mkLambdaFVars xs hx))
+          return none
+    else if root.interpreted then
+      if (← normLitValue root.self) != (← normLitValue rhs) then
+        let hne ← mkDecideProof (mkNot (← mkEq root.self rhs))
+        return some (mkApp hne h)
+      else
+        return none
+    else
+      return none
+
+/-- Propagates `MatchCond` upwards -/
+builtin_grind_propagator propagateMatchCond ↑Grind.MatchCond := fun e => do
+  trace[grind.debug.matchCond] "visiting{indentExpr e}"
+  if !(← isStatisfied e) then return ()
+  let some h ← mkMathCondProof? e
+     | reportIssue m!"failed to construct proof for{indentExpr e}"; return ()
+  trace[grind.debug.matchCond] "{← inferType h}"
+  pushEqTrue e <| mkEqTrueCore e h
+
+end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/SimpUtil.lean b/src/Lean/Meta/Tactic/Grind/SimpUtil.lean
index 4473ebdfd245..d08f8d609b0c 100644
--- a/src/Lean/Meta/Tactic/Grind/SimpUtil.lean
+++ b/src/Lean/Meta/Tactic/Grind/SimpUtil.lean
@@ -7,6 +7,7 @@ prelude
 import Lean.Meta.Tactic.Simp.Simproc
 import Lean.Meta.Tactic.Grind.Simp
 import Lean.Meta.Tactic.Grind.DoNotSimp
+import Lean.Meta.Tactic.Grind.MatchCond
 import Lean.Meta.Tactic.Simp.BuiltinSimprocs.List
 
 namespace Lean.Meta.Grind
@@ -24,7 +25,7 @@ def registerNormTheorems (preDeclNames : Array Name) (postDeclNames : Array Name
 
 /-- Returns the array of simprocs used by `grind`. -/
 protected def getSimprocs : MetaM (Array Simprocs) := do
-  let e ← Simp.getSEvalSimprocs
+  let s ← Simp.getSEvalSimprocs
   /-
   We don't want to apply `List.reduceReplicate` as a normalization operation in
   `grind`. Consider the following example:
@@ -38,9 +39,10 @@ protected def getSimprocs : MetaM (Array Simprocs) := do
   ```
   We don't want it to be simplified to `[] = []`.
   -/
-  let e := e.erase ``List.reduceReplicate
-  let e ← addDoNotSimp e
-  return #[e]
+  let s := s.erase ``List.reduceReplicate
+  let s ← addDoNotSimp s
+  let s ← addMatchCond s
+  return #[s]
 
 /-- Returns the simplification context used by `grind`. -/
 protected def getSimpContext : MetaM Simp.Context := do
diff --git a/tests/lean/run/grind_match_eq_propagation.lean b/tests/lean/run/grind_match_eq_propagation.lean
new file mode 100644
index 000000000000..05d364fb6b5a
--- /dev/null
+++ b/tests/lean/run/grind_match_eq_propagation.lean
@@ -0,0 +1,47 @@
+inductive S where
+  | mk1 (n : Nat)
+  | mk2 (n : Nat) (s : S)
+  | mk3 (n : Bool)
+  | mk4 (s1 s2 : S)
+
+def f (x y : S) :=
+  match x, y with
+  | .mk1 _, _ => 2
+  | _, .mk2 1 (.mk4 _ _) => 3
+  | .mk3 _, _ => 4
+  | _, _ => 5
+
+example : f a b < 2 → b = .mk2 y1 y2 → y1 = 2 → a = .mk4 y3 y4 → False := by
+  unfold f
+  grind (splits := 0)
+
+example : b = .mk2 y1 y2 → y1 = 2 → a = .mk4 y3 y4 → f a b = 5 := by
+  unfold f
+  grind (splits := 0)
+
+example : b = .mk2 y1 y2 → y1 = 2 → a = .mk3 n → f a b = 4 := by
+  unfold f
+  grind (splits := 0)
+
+example : b = .mk2 y1 y2 → y1 = 1 → y2 = .mk4 s1 s2 → a = .mk3 n → f a b = 3 := by
+  unfold f
+  grind (splits := 0)
+
+example : b = .mk2 y1 y2 → y1 = 1 → y2 = .mk4 s1 s2 → a = .mk2 s3 s4 → f a b = 3 := by
+  unfold f
+  grind (splits := 0)
+
+inductive Vec (α : Type u) : Nat → Type u
+  | nil : Vec α 0
+  | cons : α → Vec α n → Vec α (n+1)
+
+def g (v w : Vec α n) : Nat :=
+  match v, w with
+  | _, .cons _ (.cons _ _) => 20
+  | .nil, _ => 30
+  | _, _    => 40
+
+-- TODO: introduce casts while instantiating equation theorems for `g.match_1`
+-- example (a b : Vec α 2) : g a b = 20 := by
+--  unfold g
+--  grind