diff --git a/src/Lean/Elab/Tactic/Grind.lean b/src/Lean/Elab/Tactic/Grind.lean
index 2ceef07fc832..293e06197eed 100644
--- a/src/Lean/Elab/Tactic/Grind.lean
+++ b/src/Lean/Elab/Tactic/Grind.lean
@@ -26,7 +26,7 @@ def elabGrindPattern : CommandElab := fun stx => do
           let pattern ← instantiateMVars (← elabTerm term none)
           let pattern ← Grind.unfoldReducible pattern
           return pattern.abstract xs
-        Grind.addTheoremPattern declName xs.size patterns.toList
+        Grind.addEMatchTheorem declName xs.size patterns.toList
   | _ => throwUnsupportedSyntax
 
 def grind (mvarId : MVarId) (mainDeclName : Name) : MetaM Unit := do
diff --git a/src/Lean/Meta/Tactic/Grind.lean b/src/Lean/Meta/Tactic/Grind.lean
index 4013ab8d4b37..fb945ab507d4 100644
--- a/src/Lean/Meta/Tactic/Grind.lean
+++ b/src/Lean/Meta/Tactic/Grind.lean
@@ -21,7 +21,7 @@ import Lean.Meta.Tactic.Grind.PP
 import Lean.Meta.Tactic.Grind.Simp
 import Lean.Meta.Tactic.Grind.Ctor
 import Lean.Meta.Tactic.Grind.Parser
-import Lean.Meta.Tactic.Grind.TheoremPatterns
+import Lean.Meta.Tactic.Grind.EMatchTheorem
 
 namespace Lean
 
diff --git a/src/Lean/Meta/Tactic/Grind/TheoremPatterns.lean b/src/Lean/Meta/Tactic/Grind/EMatchTheorem.lean
similarity index 90%
rename from src/Lean/Meta/Tactic/Grind/TheoremPatterns.lean
rename to src/Lean/Meta/Tactic/Grind/EMatchTheorem.lean
index 82833aad3671..968293d2cd5f 100644
--- a/src/Lean/Meta/Tactic/Grind/TheoremPatterns.lean
+++ b/src/Lean/Meta/Tactic/Grind/EMatchTheorem.lean
@@ -25,7 +25,15 @@ inductive Origin where
   | other
   deriving Inhabited, Repr
 
-structure TheoremPattern where
+/-- A unique identifier corresponding to the origin. -/
+def Origin.key : Origin → Name
+  | .decl declName => declName
+  | .fvar fvarId   => fvarId.name
+  | .stx id _      => id
+  | .other         => `other
+
+/-- A theorem for heuristic instantiation based on E-matching. -/
+structure EMatchTheorem where
   proof       : Expr
   numParams   : Nat
   patterns    : List Expr
@@ -34,16 +42,21 @@ structure TheoremPattern where
   origin      : Origin
   deriving Inhabited
 
-abbrev TheoremPatterns := SMap Name (List TheoremPattern)
+/-- The key is a symbol from `EMatchTheorem.symbols`. -/
+abbrev EMatchTheorems := PHashMap Name (List EMatchTheorem)
 
-builtin_initialize theoremPatternsExt : SimpleScopedEnvExtension TheoremPattern TheoremPatterns ←
+def EMatchTheorems.insert (s : EMatchTheorems) (thm : EMatchTheorem) : EMatchTheorems := Id.run do
+  let .const declName :: syms := thm.symbols
+    | unreachable!
+  let thm := { thm with symbols := syms }
+  if let some thms := s.find? declName then
+    return PersistentHashMap.insert s declName (thm::thms)
+  else
+    return PersistentHashMap.insert s declName [thm]
+
+private builtin_initialize ematchTheoremsExt : SimpleScopedEnvExtension EMatchTheorem EMatchTheorems ←
   registerSimpleScopedEnvExtension {
-    addEntry := fun s t => Id.run do
-      let .const declName :: _ := t.symbols | unreachable!
-      if let some ts := s.find? declName then
-        s.insert declName (t::ts)
-      else
-        s.insert declName [t]
+    addEntry := EMatchTheorems.insert
     initial  := .empty
   }
 
@@ -282,19 +295,23 @@ private def ppParamsAt (proof : Expr) (numParms : Nat) (paramPos : List Nat) : M
         msg := msg ++ m!"{x} : {← inferType x}"
     addMessageContextFull msg
 
-def addTheoremPattern (declName : Name) (numParams : Nat) (patterns : List Expr) : MetaM Unit := do
+def addEMatchTheorem (declName : Name) (numParams : Nat) (patterns : List Expr) : MetaM Unit := do
   let .thmInfo info ← getConstInfo declName
     | throwError "`{declName}` is not a theorem, you cannot assign patterns to non-theorems for the `grind` tactic"
   let us := info.levelParams.map mkLevelParam
   let proof := mkConst declName us
   let (patterns, symbols, bvarFound) ← NormalizePattern.main patterns
+  assert! symbols.all fun s => s matches .const _
   trace[grind.pattern] "{declName}: {patterns.map ppPattern}"
   if let .missing pos ← checkCoverage proof numParams bvarFound then
      let pats : MessageData := m!"{patterns.map ppPattern}"
      throwError "invalid pattern(s) for `{declName}`{indentD pats}\nthe following theorem parameters cannot be instantiated:{indentD (← ppParamsAt proof numParams pos)}"
-  theoremPatternsExt.add {
+  ematchTheoremsExt.add {
      proof, patterns, numParams, symbols
      origin := .decl declName
   }
 
+def getEMatchTheorems : CoreM EMatchTheorems :=
+  return ematchTheoremsExt.getState (← getEnv)
+
 end Lean.Meta.Grind
diff --git a/src/Lean/Meta/Tactic/Grind/Internalize.lean b/src/Lean/Meta/Tactic/Grind/Internalize.lean
index 32d1de928af2..42a48cc7f364 100644
--- a/src/Lean/Meta/Tactic/Grind/Internalize.lean
+++ b/src/Lean/Meta/Tactic/Grind/Internalize.lean
@@ -37,6 +37,21 @@ private def updateAppMap (e : Expr) : GoalM Unit := do
       s.appMap.insert key [e]
   }
 
+private def activateTheoremPatterns (fName : Name) : GoalM Unit := do
+  if let some thms := (← get).thmMap.find? fName then
+    modify fun s => { s with thmMap := s.thmMap.erase fName }
+    let appMap := (← get).appMap
+    for thm in thms do
+      let symbols := thm.symbols.filter fun sym => !appMap.contains sym
+      let thm := { thm with symbols }
+      match symbols with
+      | [] =>
+        trace[grind.pattern] "activated `{thm.origin.key}`"
+        modify fun s => { s with newThms := s.newThms.push thm }
+      | _ =>
+        trace[grind.pattern] "reinsert `{thm.origin.key}`"
+        modify fun s => { s with thmMap := s.thmMap.insert thm }
+
 partial def internalize (e : Expr) (generation : Nat) : GoalM Unit := do
   if (← alreadyInternalized e) then return ()
   match e with
@@ -63,7 +78,9 @@ partial def internalize (e : Expr) (generation : Nat) : GoalM Unit := do
         internalize c generation
         registerParent e c
       else
-        unless f.isConst do
+        if let .const fName _ := f then
+          activateTheoremPatterns fName
+        else
           internalize f generation
           registerParent e f
         for h : i in [: args.size] do
diff --git a/src/Lean/Meta/Tactic/Grind/Run.lean b/src/Lean/Meta/Tactic/Grind/Run.lean
index f2b534b4557e..e36c3437d813 100644
--- a/src/Lean/Meta/Tactic/Grind/Run.lean
+++ b/src/Lean/Meta/Tactic/Grind/Run.lean
@@ -46,7 +46,8 @@ def GrindM.run (x : GrindM α) (mainDeclName : Name) : MetaM α := do
 def mkGoal (mvarId : MVarId) : GrindM Goal := do
   let trueExpr ← getTrueExpr
   let falseExpr ← getFalseExpr
-  GoalM.run' { mvarId } do
+  let thmMap ← getEMatchTheorems
+  GoalM.run' { mvarId, thmMap } do
     mkENodeCore falseExpr (interpreted := true) (ctor := false) (generation := 0)
     mkENodeCore trueExpr (interpreted := true) (ctor := false) (generation := 0)
 
diff --git a/src/Lean/Meta/Tactic/Grind/Types.lean b/src/Lean/Meta/Tactic/Grind/Types.lean
index edc96c5db537..0342646871a3 100644
--- a/src/Lean/Meta/Tactic/Grind/Types.lean
+++ b/src/Lean/Meta/Tactic/Grind/Types.lean
@@ -13,6 +13,7 @@ import Lean.Meta.Tactic.Simp.Types
 import Lean.Meta.Tactic.Util
 import Lean.Meta.Tactic.Grind.Canon
 import Lean.Meta.Tactic.Grind.Attr
+import Lean.Meta.Tactic.Grind.EMatchTheorem
 
 namespace Lean.Meta.Grind
 
@@ -273,6 +274,15 @@ structure Goal where
   gmt          : Nat := 0
   /-- Next unique index for creating ENodes -/
   nextIdx      : Nat := 0
+  /-- Active theorems that we have performed ematching at least once. -/
+  thms         : PArray EMatchTheorem := {}
+  /-- Active theorems that we have not performed any round of ematching yet. -/
+  newThms      : PArray EMatchTheorem := {}
+  /--
+  Inactive global theorems. As we internalize terms, we activate theorems as we find their symbols.
+  Local theorem provided by users are added directly into `newThms`.
+  -/
+  thmMap       : EMatchTheorems
   deriving Inhabited
 
 def Goal.admit (goal : Goal) : MetaM Unit :=
diff --git a/tests/lean/run/grind_pattern2.lean b/tests/lean/run/grind_pattern2.lean
new file mode 100644
index 000000000000..4b091799de3f
--- /dev/null
+++ b/tests/lean/run/grind_pattern2.lean
@@ -0,0 +1,39 @@
+def Set (α : Type) := α → Bool
+
+def insertElem [DecidableEq α] (s : Set α) (a : α) : Set α :=
+  fun x => a = x || s x
+
+def contains (s : Set α) (a : α) : Bool :=
+  s a
+
+theorem contains_insert [DecidableEq α] (s : Set α) (a : α) : contains (insertElem s a) a := by
+  simp [contains, insertElem]
+
+grind_pattern contains_insert => contains (insertElem s a) a
+
+-- TheoremPattern activation test
+
+set_option trace.grind.pattern true
+
+/--
+warning: declaration uses 'sorry'
+---
+info: [grind.pattern] activated `contains_insert`
+-/
+#guard_msgs 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
+
+/--
+warning: declaration uses 'sorry'
+---
+info: [grind.pattern] reinsert `contains_insert`
+[grind.pattern] activated `contains_insert`
+-/
+#guard_msgs 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