feat: add grind core module (#4249)

src/Init/Grind.lean

@@ -7,3 +7,4 @@ prelude
 import Init.Grind.Norm
 import Init.Grind.Tactics
 import Init.Grind.Lemmas
+import Init.Grind.Cases

src/Init/Grind/Cases.lean

@@ -0,0 +1,15 @@
+/-
+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.Core
+
+attribute [grind_cases] And Prod False Empty True Unit Exists
+
+namespace Lean.Grind.Eager
+
+attribute [scoped grind_cases] Or
+
+end Lean.Grind.Eager

src/Init/Grind/Tactics.lean

@@ -7,8 +7,19 @@ prelude
 import Init.Tactics
 
 namespace Lean.Grind
+/--
+The configuration for `grind`.
+Passed to `grind` using, for example, the `grind (config := { eager := true })` syntax.
+-/
+structure Config where
+  /--
+  When `eager` is true (default: `false`), `grind` eagerly splits `if-then-else` and `match`
+  expressions.
+  -/
+  eager : Bool := false
+  deriving Inhabited, BEq
+
 /-!
 `grind` tactic and related tactics.
 -/
-
 end Lean.Grind

src/Lean/Meta/LitValues.lean

@@ -99,6 +99,8 @@ def getUInt64Value? (e : Expr) : MetaM (Option UInt64) := OptionT.run do
   let (n, _) ← getOfNatValue? e ``UInt64
   return UInt64.ofNat n
 
+-- TODO: extensibility
+
 /--
 If `e` is a literal value, ensure it is encoded using the standard representation.
 Otherwise, just return `e`.
@@ -117,6 +119,23 @@ def normLitValue (e : Expr) : MetaM Expr := do
   if let some n ← getUInt64Value? e then return toExpr n
   return e
 
+/--
+Returns `true` if `e` is a literal value.
+-/
+def isLitValue (e : Expr) : MetaM Bool := do
+  let e ← instantiateMVars e
+  if (← getNatValue? e).isSome then return true
+  if (← getIntValue? e).isSome then return true
+  if (← getFinValue? e).isSome then return true
+  if (← getBitVecValue? e).isSome then return true
+  if (getStringValue? e).isSome then return true
+  if (← getCharValue? e).isSome then return true
+  if (← getUInt8Value? e).isSome then return true
+  if (← getUInt16Value? e).isSome then return true
+  if (← getUInt32Value? e).isSome then return true
+  if (← getUInt64Value? e).isSome then return true
+  return false
+
 /--
 If `e` is a `Nat`, `Int`, or `Fin` literal value, converts it into a constructor application.
 Otherwise, just return `e`.

src/Lean/Meta/Tactic/Grind.lean

@@ -11,3 +11,4 @@ import Lean.Meta.Tactic.Grind.Preprocessor
 import Lean.Meta.Tactic.Grind.Util
 import Lean.Meta.Tactic.Grind.Cases
 import Lean.Meta.Tactic.Grind.Injection
+import Lean.Meta.Tactic.Grind.Core

src/Lean/Meta/Tactic/Grind/Core.lean

@@ -0,0 +1,157 @@
+/-
+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 Lean.Meta.Tactic.Grind.Types
+import Lean.Meta.LitValues
+
+namespace Lean.Meta.Grind
+/--
+Returns `true` if `e` is `True`, `False`, or a literal value.
+See `LitValues` for supported literals.
+-/
+def isInterpreted (e : Expr) : MetaM Bool := do
+  if e.isTrue || e.isFalse then return true
+  isLitValue e
+
+/--
+Creates an `ENode` for `e` if one does not already exist.
+This method assumes `e` has been hashconsed.
+-/
+def mkENode (e : Expr) (generation : Nat := 0) : GoalM Unit := do
+  if (← getENode? e).isSome then return ()
+  let ctor := (← isConstructorAppCore? e).isSome
+  let interpreted ← isInterpreted e
+  mkENodeCore e interpreted ctor generation
+
+/--
+Returns the root element in the equivalence class of `e`.
+-/
+def getRoot (e : Expr) : GoalM Expr := do
+  let some n ← getENode? e | return e
+  return n.root
+
+/--
+Returns the next element in the equivalence class of `e`.
+-/
+def getNext (e : Expr) : GoalM Expr := do
+  let some n ← getENode? e | return e
+  return n.next
+
+@[inline] def isSameExpr (a b : Expr) : Bool :=
+  -- It is safe to use pointer equality because we hashcons all expressions
+  -- inserted into the E-graph
+  unsafe ptrEq a b
+
+private def pushNewEqCore (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit :=
+  modify fun s => { s with newEqs := s.newEqs.push { lhs, rhs, proof, isHEq } }
+
+@[inline] private def pushNewEq (lhs rhs proof : Expr) : GoalM Unit :=
+  pushNewEqCore lhs rhs proof (isHEq := false)
+
+@[inline] private def pushNewHEq (lhs rhs proof : Expr) : GoalM Unit :=
+  pushNewEqCore lhs rhs proof (isHEq := true)
+
+/--
+The fields `target?` and `proof?` in `e`'s `ENode` are encoding a transitivity proof
+from `e` to the root of the equivalence class
+This method "inverts" the proof, and makes it to go from the root of the equivalence class to `e`.
+
+We use this method when merging two equivalence classes.
+-/
+private partial def invertTrans (e : Expr) : GoalM Unit := do
+  go e false none none
+where
+  go (e : Expr) (flippedNew : Bool) (targetNew? : Option Expr) (proofNew? : Option Expr) : GoalM Unit := do
+    let some node ← getENode? e | unreachable!
+    if let some target := node.target? then
+      go target (!node.flipped) (some e) node.proof?
+    setENode e { node with
+      target? := targetNew?
+      flipped := flippedNew
+      proof?  := proofNew?
+    }
+
+private def markAsInconsistent : GoalM Unit :=
+  modify fun s => { s with inconsistent := true }
+
+private partial def addEqStep (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit := do
+  let some lhsNode ← getENode? lhs | return () -- `lhs` has not been internalized yet
+  let some rhsNode ← getENode? rhs | return () -- `rhs` has not been internalized yet
+  if isSameExpr lhsNode.root rhsNode.root then return () -- `lhs` and `rhs` are already in the same equivalence class.
+  let some lhsRoot ← getENode? lhsNode.root | unreachable!
+  let some rhsRoot ← getENode? rhsNode.root | unreachable!
+  if    (lhsRoot.interpreted && !rhsRoot.interpreted)
+     || (lhsRoot.ctor && !rhsRoot.ctor)
+     || (lhsRoot.size > rhsRoot.size && !rhsRoot.interpreted && !rhsRoot.ctor) then
+    go rhs lhs rhsNode lhsNode rhsRoot lhsRoot true
+  else
+    go lhs rhs lhsNode rhsNode lhsRoot rhsRoot false
+where
+  go (lhs rhs : Expr) (lhsNode rhsNode lhsRoot rhsRoot : ENode) (flipped : Bool) : GoalM Unit := do
+    let mut valueInconsistency := false
+    if lhsRoot.interpreted && rhsRoot.interpreted then
+      if lhsNode.root.isTrue || rhsNode.root.isTrue then
+        markAsInconsistent
+      else
+        valueInconsistency := true
+    -- TODO: process valueInconsistency := true
+    /-
+    We have the following `target?/proof?`
+    `lhs -> ... -> lhsNode.root`
+    `rhs -> ... -> rhsNode.root`
+    We want to convert it to
+    `lhsNode.root -> ... -> lhs -*-> rhs -> ... -> rhsNode.root`
+    where step `-*->` is justified by `proof` (or `proof.symm` if `flipped := true`)
+    -/
+    invertTrans lhs
+    setENode lhs { lhsNode with
+      target? := rhs
+      proof?  := proof
+      flipped
+    }
+    -- TODO: Remove parents from congruence table
+    -- TODO: set propagateBool
+    updateRoots lhs rhsNode.root true -- TODO
+    -- TODO: Reinsert parents into congruence table
+    setENode lhsNode.root { lhsRoot with
+      next := rhsRoot.next
+    }
+    setENode rhsNode.root { rhsRoot with
+      next := lhsRoot.next
+      size := rhsRoot.size + lhsRoot.size
+      hasLambdas := rhsRoot.hasLambdas || lhsRoot.hasLambdas
+      heqProofs  := isHEq || rhsRoot.heqProofs || lhsRoot.heqProofs
+    }
+    -- TODO: copy parentst from lhsRoot parents to rhsRoot parents
+
+  updateRoots (lhs : Expr) (rootNew : Expr) (_propagateBool : Bool) : GoalM Unit := do
+    let rec loop (e : Expr) : GoalM Unit := do
+      -- TODO: propagateBool
+      let some n ← getENode? e | unreachable!
+      setENode e { n with root := rootNew }
+      if isSameExpr lhs n.next then return ()
+      loop n.next
+    loop lhs
+
+partial def addEqCore (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit := do
+  addEqStep lhs rhs proof isHEq
+  processTodo
+where
+  processTodo : GoalM Unit := do
+    if (← get).inconsistent then
+      modify fun s => { s with newEqs := #[] }
+      return ()
+    let some { lhs, rhs, proof, isHEq } := (← get).newEqs.back? | return ()
+    addEqStep lhs rhs proof isHEq
+    processTodo
+
+def addEq (lhs rhs proof : Expr) : GoalM Unit := do
+  addEqCore lhs rhs proof false
+
+def addHEq (lhs rhs proof : Expr) : GoalM Unit := do
+  addEqCore lhs rhs proof true
+
+end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Preprocessor.lean

@@ -15,6 +15,7 @@ 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
 
 namespace Lean.Meta.Grind
 namespace Preprocessor
@@ -29,6 +30,7 @@ structure Context where
 
 structure State where
   simpStats : Simp.Stats := {}
+  goals     : PArray Goal := {}
   deriving Inhabited
 
 abbrev PreM := ReaderT Context $ StateRefT State GrindM
@@ -43,18 +45,13 @@ def PreM.run (x : PreM α) : GrindM α := do
   }
   x { simp, simprocs } |>.run' {}
 
-def simp (e : Expr) : PreM Simp.Result := do
+def simp (_goal : Goal) (e : Expr) : PreM Simp.Result := do
+  -- TODO: use `goal` state in the simplifier
   let simpStats := (← get).simpStats
   let (r, simpStats) ← Meta.simp e (← read).simp (← read).simprocs (stats := simpStats)
   modify fun s => { s with simpStats }
   return r
 
-def simpHyp? (mvarId : MVarId) (fvarId : FVarId) : PreM (Option (FVarId × MVarId)) := do
-  let simpStats := (← get).simpStats
-  let (result, simpStats) ← simpLocalDecl mvarId fvarId (← read).simp (← read).simprocs (stats := simpStats)
-  modify fun s => { s with simpStats }
-  return result
-
 inductive IntroResult where
   | done
   | newHyp (fvarId : FVarId) (goal : Goal)
@@ -72,7 +69,7 @@ def introNext (goal : Goal) : PreM IntroResult := do
       else
         let tag ← goal.mvarId.getTag
         let q := target.bindingBody!
-        let r ← simp p
+        let r ← simp goal p
         let p' := r.expr
         let p' ← canon p'
         let p' ← shareCommon p'
@@ -105,7 +102,7 @@ def introNext (goal : Goal) : PreM IntroResult := do
     return .done
 
 def pushResult (goal : Goal) : PreM Unit :=
-  modifyThe Grind.State fun s => { s with goals := s.goals.push goal }
+  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
@@ -124,42 +121,47 @@ def applyInjection? (goal : Goal) (fvarId : FVarId) : MetaM (Option Goal) := do
   else
     return none
 
-partial def preprocess (goal : Goal) : PreM Unit := do
+partial def loop (goal : Goal) : PreM Unit := do
   match (← introNext goal) with
   | .done =>
     if let some mvarId ← goal.mvarId.byContra? then
-      preprocess { goal with mvarId }
+      loop { goal with mvarId }
     else
       pushResult goal
   | .newHyp fvarId goal =>
     if let some goals ← applyCases? goal fvarId then
-      goals.forM preprocess
+      goals.forM loop
     else if let some goal ← applyInjection? goal fvarId then
-      preprocess goal
+      loop goal
     else
       let clause ← goal.mvarId.withContext do mkInputClause fvarId
-      preprocess { goal with clauses := goal.clauses.push clause }
+      loop { goal with clauses := goal.clauses.push clause }
   | .newDepHyp goal =>
-    preprocess goal
+    loop goal
   | .newLocal fvarId goal =>
     if let some goals ← applyCases? goal fvarId then
-      goals.forM preprocess
+      goals.forM loop
     else
-      preprocess goal
+      loop goal
+
+def preprocess (mvarId : MVarId) : PreM State := do
+  loop (← mkGoal mvarId)
+  get
 
 end Preprocessor
 
 open Preprocessor
 
-partial def main (mvarId : MVarId) (mainDeclName : Name) : MetaM Grind.State := do
+partial def main (mvarId : MVarId) (mainDeclName : Name) : MetaM (List MVarId) := do
   mvarId.ensureProp
   mvarId.ensureNoMVar
+  let mvarId ← mvarId.clearAuxDecls
   let mvarId ← mvarId.revertAll
   mvarId.ensureNoMVar
   let mvarId ← mvarId.abstractNestedProofs mainDeclName
   let mvarId ← mvarId.unfoldReducible
   let mvarId ← mvarId.betaReduce
-  let s ← (preprocess { mvarId } *> getThe Grind.State) |>.run |>.run mainDeclName
-  return s
+  let s ← preprocess mvarId |>.run |>.run mainDeclName
+  return s.goals.toList.map (·.mvarId)
 
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Types.lean

@@ -11,6 +11,47 @@ import Lean.Meta.Canonicalizer
 import Lean.Meta.Tactic.Util
 
 namespace Lean.Meta.Grind
+
+structure Context where
+  mainDeclName : Name
+
+structure State where
+  canon      : Canonicalizer.State := {}
+  /-- `ShareCommon` (aka `Hashconsing`) state. -/
+  scState    : ShareCommon.State.{0} ShareCommon.objectFactory := ShareCommon.State.mk _
+  /-- Next index for creating auxiliary theorems. -/
+  nextThmIdx : Nat := 1
+
+abbrev GrindM := ReaderT Context $ StateRefT State MetaM
+
+@[inline] def GrindM.run (x : GrindM α) (mainDeclName : Name) : MetaM α :=
+  x { mainDeclName } |>.run' {}
+
+def abstractNestedProofs (e : Expr) : GrindM Expr := do
+  let nextIdx := (← get).nextThmIdx
+  let (e, s') ← AbstractNestedProofs.visit e |>.run { baseName := (← read).mainDeclName } |>.run |>.run { nextIdx }
+  modify fun s => { s with nextThmIdx := s'.nextIdx }
+  return e
+
+def shareCommon (e : Expr) : GrindM Expr := do
+  modifyGet fun { canon, scState, nextThmIdx } =>
+    let (e, scState) := ShareCommon.State.shareCommon scState e
+    (e, { canon, scState, nextThmIdx })
+
+def canon (e : Expr) : GrindM Expr := do
+  let canonS ← modifyGet fun s => (s.canon, { s with canon := {} })
+  let (e, canonS) ← Canonicalizer.CanonM.run (canonRec e) (s := canonS)
+  modify fun s => { s with canon := canonS }
+  return e
+where
+  canonRec (e : Expr) : CanonM Expr := do
+    let post (e : Expr) : CanonM TransformStep := do
+      if e.isApp then
+        return .done (← Meta.canon e)
+      else
+        return .done e
+    transform e post
+
 /--
 Stores information for a node in the egraph.
 Each internalized expression `e` has an `ENode` associated with it.
@@ -43,6 +84,9 @@ structure ENode where
   on heterogeneous equality.
   -/
   heqProofs : Bool := false
+  generation : Nat := 0
+  /-- Modification time -/
+  mt : Nat := 0
   -- TODO: see Lean 3 implementation
 
 structure Clause where
@@ -53,58 +97,57 @@ structure Clause where
 def mkInputClause (fvarId : FVarId) : MetaM Clause :=
   return { expr := (← fvarId.getType), proof := mkFVar fvarId }
 
-structure Goal where
-  mvarId  : MVarId
-  clauses : PArray Clause := {}
-  enodes  : PHashMap UInt64 ENode := {}
-  -- TODO: occurrences for propagation, etc
-  deriving Inhabited
+structure NewEq where
+  lhs   : Expr
+  rhs   : Expr
+  proof : Expr
+  isHEq : Bool
 
-def mkGoal (mvarId : MVarId) : Goal :=
-  { mvarId }
+structure Goal where
+  mvarId       : MVarId
+  clauses      : PArray Clause := {}
+  enodes       : PHashMap USize ENode := {}
+  newEqs       : Array NewEq := #[]
+  /-- `inconsistent := true` if `ENode`s for `True` and `False` are in the same equivalence class. -/
+  inconsistent : Bool := false
+  /-- Goal modification time. -/
+  gmt          : Nat := 0
+  deriving Inhabited
 
 def Goal.admit (goal : Goal) : MetaM Unit :=
   goal.mvarId.admit
 
-structure Context where
-  mainDeclName : Name
+abbrev GoalM := StateRefT Goal GrindM
 
-structure State where
-  canon      : Canonicalizer.State := {}
-  /-- `ShareCommon` (aka `Hashconsing`) state. -/
-  scState    : ShareCommon.State.{0} ShareCommon.objectFactory := ShareCommon.State.mk _
-  /-- Next index for creating auxiliary theorems. -/
-  nextThmIdx : Nat := 1
-  goals      : PArray Goal := {}
+@[inline] def GoalM.run (goal : Goal) (x : GoalM α) : GrindM (α × Goal) :=
+  StateRefT'.run x goal
 
-abbrev GrindM := ReaderT Context $ StateRefT State MetaM
+@[inline] def GoalM.run' (goal : Goal) (x : GoalM Unit) : GrindM Goal :=
+  StateRefT'.run' (x *> get) goal
 
-def GrindM.run (x : GrindM α) (mainDeclName : Name) : MetaM α :=
-  x { mainDeclName } |>.run' {}
+/--
+Returns `some n` if `e` has already been "internalized" into the
+Otherwise, returns `none`s.
+-/
+def getENode? (e : Expr) : GoalM (Option ENode) :=
+  return (← get).enodes.find? (unsafe ptrAddrUnsafe e)
 
-def abstractNestedProofs (e : Expr) : GrindM Expr := do
-  let nextIdx := (← get).nextThmIdx
-  let (e, s') ← AbstractNestedProofs.visit e |>.run { baseName := (← read).mainDeclName } |>.run |>.run { nextIdx }
-  modify fun s => { s with nextThmIdx := s'.nextIdx }
-  return e
+def setENode (e : Expr) (n : ENode) : GoalM Unit :=
+  modify fun s => { s with enodes := s.enodes.insert (unsafe ptrAddrUnsafe e) n }
 
-def shareCommon (e : Expr) : GrindM Expr := do
-  modifyGet fun { canon, scState, nextThmIdx, goals } =>
-    let (e, scState) := ShareCommon.State.shareCommon scState e
-    (e, { canon, scState, nextThmIdx, goals })
+def mkENodeCore (e : Expr) (interpreted ctor : Bool) (generation : Nat) : GoalM Unit := do
+  setENode e {
+    next := e, root := e, cgRoot := e, size := 1
+    flipped := false
+    heqProofs := false
+    hasLambdas := e.isLambda
+    mt := (← get).gmt
+    interpreted, ctor, generation
+  }
 
-def canon (e : Expr) : GrindM Expr := do
-  let canonS ← modifyGet fun s => (s.canon, { s with canon := {} })
-  let (e, canonS) ← Canonicalizer.CanonM.run (canonRec e) (s := canonS)
-  modify fun s => { s with canon := canonS }
-  return e
-where
-  canonRec (e : Expr) : CanonM Expr := do
-    let post (e : Expr) : CanonM TransformStep := do
-      if e.isApp then
-        return .done (← Meta.canon e)
-      else
-        return .done e
-    transform e post
+def mkGoal (mvarId : MVarId) : GrindM Goal := do
+  GoalM.run' { mvarId } do
+    mkENodeCore (← shareCommon (mkConst ``True)) (interpreted := true) (ctor := false) (generation := 0)
+    mkENodeCore (← shareCommon (mkConst ``False)) (interpreted := true) (ctor := false) (generation := 0)
 
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Util.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Lean.Meta.AbstractNestedProofs
 import Lean.Meta.Tactic.Util
+import Lean.Meta.Tactic.Clear
 
 namespace Lean.Meta.Grind
 /--
@@ -66,7 +67,7 @@ def _root_.Lean.MVarId.betaReduce (mvarId : MVarId) : MetaM MVarId :=
 If the target is not `False`, apply `byContradiction`.
 -/
 def _root_.Lean.MVarId.byContra? (mvarId : MVarId) : MetaM (Option MVarId) := mvarId.withContext do
-  mvarId.checkNotAssigned `grind
+  mvarId.checkNotAssigned `grind.by_contra
   let target ← mvarId.getType
   if target.isFalse then return none
   let targetNew ← mkArrow (mkNot target) (mkConst ``False)
@@ -75,4 +76,24 @@ def _root_.Lean.MVarId.byContra? (mvarId : MVarId) : MetaM (Option MVarId) := mv
   mvarId.assign <| mkApp2 (mkConst ``Classical.byContradiction) target mvarNew
   return mvarNew.mvarId!
 
+/--
+Clear auxiliary decls used to encode recursive declarations.
+`grind` eliminates them to ensure they are not accidentaly used by its proof automation.
+-/
+def _root_.Lean.MVarId.clearAuxDecls (mvarId : MVarId) : MetaM MVarId := mvarId.withContext do
+  mvarId.checkNotAssigned `grind.clear_aux_decls
+  let mut toClear := []
+  for localDecl in (← getLCtx) do
+    if localDecl.isAuxDecl then
+      toClear := localDecl.fvarId :: toClear
+  if toClear.isEmpty then
+    return mvarId
+  let mut mvarId := mvarId
+  for fvarId in toClear do
+    try
+      mvarId ← mvarId.clear fvarId
+    catch _ =>
+      throwTacticEx `grind.clear_aux_decls mvarId "failed to clear local auxiliary declaration"
+  return mvarId
+
 end Lean.Meta.Grind

tests/lean/run/grind_pre.lean

@@ -4,13 +4,29 @@ open Lean Meta Elab Tactic Grind in
 elab "grind_pre" : tactic => do
   let declName := (← Term.getDeclName?).getD `_main
   liftMetaTactic fun mvarId => do
-    let result ← Meta.Grind.main mvarId declName
-    return result.goals.map (·.mvarId) |>.toList
+    Meta.Grind.main mvarId declName
 
 abbrev f (a : α) := a
 
-attribute [grind_cases] And Or
+/--
+warning: declaration uses 'sorry'
+---
+info: a b c : Bool
+p q : Prop
+left✝ : a = true
+right✝ : b = true ∨ c = true
+left : p
+right : q
+x✝ : b = false ∨ a = false
+⊢ False
+-/
+#guard_msgs in
+theorem ex (h : (f a && (b || f (f c))) = true) (h' : p ∧ q) : b && a := by
+  grind_pre
+  trace_state
+  all_goals sorry
 
+open Lean.Grind.Eager in
 /--
 warning: declaration uses 'sorry'
 ---
@@ -51,11 +67,12 @@ h : a = false
 ⊢ False
 -/
 #guard_msgs in
-theorem ex (h : (f a && (b || f (f c))) = true) (h' : p ∧ q) : b && a := by
+theorem ex2 (h : (f a && (b || f (f c))) = true) (h' : p ∧ q) : b && a := by
   grind_pre
   trace_state
   all_goals sorry
 
+
 def g (i : Nat) (j : Nat) (_ : i > j := by omega) := i + j
 
 example (i j : Nat) (h : i + 1 > j + 1) : g (i+1) j = f ((fun x => x) i) + f j + 1 := by
@@ -65,27 +82,29 @@ example (i j : Nat) (h : i + 1 > j + 1) : g (i+1) j = f ((fun x => x) i) + f j +
   guard_hyp hn : ¬g (i + 1) j _ = i + j + 1
   simp_arith [g] at hn
 
+structure Point where
+  x : Nat
+  y : Int
+
 /--
 warning: declaration uses 'sorry'
 ---
-info: α✝ : Type u_1
-β✝ : Type u_2
-a₁ : α✝ × β✝
-a₂ : α✝
-a₃ : β✝
-as : List (α✝ × β✝)
-b₁ : α✝ × β✝
-b₂ : α✝
-b₃ : β✝
-bs : List (α✝ × β✝)
+info: a₁ : Point
+a₂ : Nat
+a₃ : Int
+as : List Point
+b₁ : Point
+bs : List Point
+b₂ : Nat
+b₃ : Int
 head_eq : a₁ = b₁
-fst_eq : a₂ = b₂
-snd_eq : a₃ = b₃
+x_eq : a₂ = b₂
+y_eq : a₃ = b₃
 tail_eq : as = bs
 ⊢ False
 -/
 #guard_msgs in
-theorem ex2 (h : a₁ :: (a₂, a₃) :: as = b₁ :: (b₂, b₃) :: bs) : False := by
+theorem ex3 (h : a₁ :: { x := a₂, y := a₃ : Point } :: as = b₁ :: { x := b₂, y := b₃} :: bs) : False := by
   grind_pre
   trace_state
   sorry