opaque Lean.Meta.Simp.congrHypothesisExceptionId : Lean.InternalExceptionId

def Lean.Meta.Simp.throwCongrHypothesisFailed {α : Type} : Lean.MetaM α

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• Lean.Meta.Simp.throwCongrHypothesisFailed = throw (Lean.Exception.internal Lean.Meta.Simp.congrHypothesisExceptionId)

def Lean.Meta.Simp.Config.updateArith (c : Lean.Meta.Simp.Config) : Lean.CoreM Lean.Meta.Simp.Config

Helper method for bootstrapping purposes. It disables arith if support theorems have not been defined yet.

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def Lean.Meta.Simp.Result.getProof (r : Lean.Meta.Simp.Result) : Lean.MetaM Lean.Expr

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• Lean.Meta.Simp.Result.getProof r = match r.proof? with | some p => pure p | none => Lean.Meta.mkEqRefl r.expr

def Lean.Meta.Simp.Result.getProof' (source : Lean.Expr) (r : Lean.Meta.Simp.Result) : Lean.MetaM Lean.Expr

Similar to Result.getProof, but adds a mkExpectedTypeHint if proof? is none (i.e., result is definitionally equal to input), but we cannot establish that source and r.expr are definitionally when using TransparencyMode.reducible.

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def Lean.Meta.Simp.mkCongrFun (r : Lean.Meta.Simp.Result) (a : Lean.Expr) : Lean.MetaM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.mkCongr (r₁ : Lean.Meta.Simp.Result) (r₂ : Lean.Meta.Simp.Result) : Lean.MetaM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.isOfNatNatLit (e : Lean.Expr) : Bool

Return true if e is of the form ofNat n where n is a kernel Nat literal

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• Lean.Meta.Simp.isOfNatNatLit e = (Lean.Expr.isAppOfArity e `OfNat.ofNat 3 && Lean.Expr.isNatLit (Lean.Expr.appArg! (Lean.Expr.appFn! e)))

instance Lean.Meta.Simp.instInhabitedM {α : Type} : Inhabited (Lean.Meta.Simp.M α)

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• Lean.Meta.Simp.instInhabitedM = { default := fun x x x => default }

def Lean.Meta.Simp.lambdaTelescopeDSimp {α : Type} (e : Lean.Expr) (k : Array Lean.Expr → Lean.Expr → Lean.Meta.Simp.M α) : Lean.Meta.Simp.M α

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• Lean.Meta.Simp.lambdaTelescopeDSimp e k = Lean.Meta.Simp.lambdaTelescopeDSimp.go k #[] e

partial def Lean.Meta.Simp.lambdaTelescopeDSimp.go {α : Type} (k : Array Lean.Expr → Lean.Expr → Lean.Meta.Simp.M α) (xs : Array Lean.Expr) (e : Lean.Expr) : Lean.Meta.Simp.M α

inductive Lean.Meta.Simp.SimpLetCase : Type

• dep: Lean.Meta.Simp.SimpLetCase
• nondepDepVar: Lean.Meta.Simp.SimpLetCase
• nondep: Lean.Meta.Simp.SimpLetCase

def Lean.Meta.Simp.getSimpLetCase (n : Lean.Name) (t : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Meta.Simp.SimpLetCase

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def Lean.Meta.Simp.removeUnnecessaryCasts (e : Lean.Expr) : Lean.MetaM Lean.Expr

Given the application e, remove unnecessary casts of the form Eq.rec a rfl and Eq.ndrec a rfl.

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def Lean.Meta.Simp.removeUnnecessaryCasts.isDummyEqRec (e : Lean.Expr) : Bool

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• Lean.Meta.Simp.removeUnnecessaryCasts.isDummyEqRec e = ((Lean.Expr.isAppOfArity e `Eq.rec 6 || Lean.Expr.isAppOfArity e `Eq.ndrec 6) && Lean.Expr.isAppOf (Lean.Expr.appArg! e) `Eq.refl)

partial def Lean.Meta.Simp.removeUnnecessaryCasts.elimDummyEqRec (e : Lean.Expr) : Lean.Expr

partial def Lean.Meta.Simp.simp (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.simpLoop (e : Lean.Expr) (r : Lean.Meta.Simp.Result) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.simpStep (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

def Lean.Meta.Simp.simp.simpLit (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

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partial def Lean.Meta.Simp.simp.simpProj (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.congrArgs (r : Lean.Meta.Simp.Result) (args : Array Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.visitFn (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

def Lean.Meta.Simp.simp.mkCongrSimp? (f : Lean.Expr) : Lean.Meta.Simp.M (Option Lean.Meta.CongrTheorem)

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partial def Lean.Meta.Simp.simp.tryAutoCongrTheorem? (e : Lean.Expr) : Lean.Meta.Simp.M (Option Lean.Meta.Simp.Result)

Try to use automatically generated congruence theorems. See mkCongrSimp?.

partial def Lean.Meta.Simp.simp.congrDefault (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.processCongrHypothesis (h : Lean.Expr) : Lean.Meta.Simp.M Bool

Process the given congruence theorem hypothesis. Return true if it made "progress".

partial def Lean.Meta.Simp.simp.trySimpCongrTheorem? (c : Lean.Meta.SimpCongrTheorem) (e : Lean.Expr) : Lean.Meta.Simp.M (Option Lean.Meta.Simp.Result)

Try to rewrite e children using the given congruence theorem

partial def Lean.Meta.Simp.simp.congr (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.simpApp (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

def Lean.Meta.Simp.simp.simpConst (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

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• Lean.Meta.Simp.simp.simpConst e = do let __do_lift ← liftM (Lean.Meta.Simp.reduce e) pure { expr := __do_lift, proof? := none, dischargeDepth := 0 }

def Lean.Meta.Simp.simp.withNewLemmas {α : Type} (xs : Array Lean.Expr) (f : Lean.Meta.Simp.M α) : Lean.Meta.Simp.M α

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partial def Lean.Meta.Simp.simp.simpLambda (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.simpArrow (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.simpForall (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simp.simpLet (e : Lean.Expr) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

def Lean.Meta.Simp.simp.cacheResult (e : Lean.Expr) (cfg : Lean.Meta.Simp.Config) (r : Lean.Meta.Simp.Result) : Lean.Meta.Simp.M Lean.Meta.Simp.Result

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@[inline]

def Lean.Meta.Simp.withSimpConfig {α : Type} (ctx : Lean.Meta.Simp.Context) (x : Lean.MetaM α) : Lean.MetaM α

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def Lean.Meta.Simp.main (e : Lean.Expr) (ctx : Lean.Meta.Simp.Context) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) (methods : optParam Lean.Meta.Simp.Methods { pre := fun e => pure (Lean.Meta.Simp.Step.visit { expr := e, proof? := none, dischargeDepth := 0 }), post := fun e => pure (Lean.Meta.Simp.Step.done { expr := e, proof? := none, dischargeDepth := 0 }), discharge? := fun x => pure none }) : Lean.MetaM (Lean.Meta.Simp.Result × Lean.Meta.Simp.UsedSimps)

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def Lean.Meta.Simp.dsimpMain (e : Lean.Expr) (ctx : Lean.Meta.Simp.Context) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) (methods : optParam Lean.Meta.Simp.Methods { pre := fun e => pure (Lean.Meta.Simp.Step.visit { expr := e, proof? := none, dischargeDepth := 0 }), post := fun e => pure (Lean.Meta.Simp.Step.done { expr := e, proof? := none, dischargeDepth := 0 }), discharge? := fun x => pure none }) : Lean.MetaM (Lean.Expr × Lean.Meta.Simp.UsedSimps)

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def Lean.Meta.Simp.isEqnThmHypothesis (e : Lean.Expr) : Bool

Return true if e is of the form (x : α) → ... → s = t → ... → False→ ... → s = t → ... → False→ s = t → ... → False→ ... → False→ False

Recall that this kind of proposition is generated by Lean when creating equations for functions and match-expressions with overlapping cases. Example: the following match-expression has overlapping cases.

def f (x y : Nat) :=
  match x, y with
  | Nat.succ n, Nat.succ m => ...
  | _, _ => 0

The second equation is of the form

(x y : Nat) → ((n m : Nat) → x = Nat.succ n → y = Nat.succ m → False) → f x y = 0
→ ((n m : Nat) → x = Nat.succ n → y = Nat.succ m → False) → f x y = 0
→ x = Nat.succ n → y = Nat.succ m → False) → f x y = 0
→ y = Nat.succ m → False) → f x y = 0
→ False) → f x y = 0
→ f x y = 0

The hypothesis (n m : Nat) → x = Nat.succ n → y = Nat.succ m → False→ x = Nat.succ n → y = Nat.succ m → False→ y = Nat.succ m → False→ False is essentially saying the first case is not applicable.

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• Lean.Meta.Simp.isEqnThmHypothesis e = (Lean.Expr.isForall e && Lean.Meta.Simp.isEqnThmHypothesis.go e)

partial def Lean.Meta.Simp.isEqnThmHypothesis.go (e : Lean.Expr) : Bool

@[inline]

abbrev Lean.Meta.Simp.Discharge : Type

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• Lean.Meta.Simp.Discharge = (Lean.Expr → Lean.Meta.SimpM (Option Lean.Expr))

def Lean.Meta.Simp.dischargeUsingAssumption? (e : Lean.Expr) : Lean.Meta.SimpM (Option Lean.Expr)

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def Lean.Meta.Simp.dischargeEqnThmHypothesis? (e : Lean.Expr) : Lean.MetaM (Option Lean.Expr)

Tries to solve e using unifyEq?. It assumes that isEqnThmHypothesis e is true.

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partial def Lean.Meta.Simp.dischargeEqnThmHypothesis?.go? (mvarId : Lean.MVarId) : Lean.MetaM (Option Lean.MVarId)

partial def Lean.Meta.Simp.DefaultMethods.discharge? (e : Lean.Expr) : Lean.Meta.SimpM (Option Lean.Expr)

partial def Lean.Meta.Simp.DefaultMethods.pre (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Step

partial def Lean.Meta.Simp.DefaultMethods.post (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Step

def Lean.Meta.Simp.DefaultMethods.methods : Lean.Meta.Simp.Methods

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• Lean.Meta.Simp.DefaultMethods.methods = { pre := Lean.Meta.Simp.DefaultMethods.pre, post := Lean.Meta.Simp.DefaultMethods.post, discharge? := Lean.Meta.Simp.DefaultMethods.discharge? }

def Lean.Meta.simp (e : Lean.Expr) (ctx : Lean.Meta.Simp.Context) (discharge? : optParam (Option Lean.Meta.Simp.Discharge) none) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Lean.Meta.Simp.Result × Lean.Meta.Simp.UsedSimps)

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def Lean.Meta.dsimp (e : Lean.Expr) (ctx : Lean.Meta.Simp.Context) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Lean.Expr × Lean.Meta.Simp.UsedSimps)

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def Lean.Meta.applySimpResultToTarget (mvarId : Lean.MVarId) (target : Lean.Expr) (r : Lean.Meta.Simp.Result) : Lean.MetaM Lean.MVarId

Auxiliary method. Given the current target of mvarId, apply r which is a new target and proof that it is equal to the current one.

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def Lean.Meta.simpTargetCore (mvarId : Lean.MVarId) (ctx : Lean.Meta.Simp.Context) (discharge? : optParam (Option Lean.Meta.Simp.Discharge) none) (mayCloseGoal : optParam Bool true) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Option Lean.MVarId × Lean.Meta.Simp.UsedSimps)

See simpTarget. This method assumes mvarId is not assigned, and we are already using mvarIds local context.

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def Lean.Meta.simpTarget (mvarId : Lean.MVarId) (ctx : Lean.Meta.Simp.Context) (discharge? : optParam (Option Lean.Meta.Simp.Discharge) none) (mayCloseGoal : optParam Bool true) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Option Lean.MVarId × Lean.Meta.Simp.UsedSimps)

Simplify the given goal target (aka type). Return none if the goal was closed. Return some mvarId' otherwise, where mvarId' is the simplified new goal.

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def Lean.Meta.applySimpResultToProp (mvarId : Lean.MVarId) (proof : Lean.Expr) (prop : Lean.Expr) (r : Lean.Meta.Simp.Result) (mayCloseGoal : optParam Bool true) : Lean.MetaM (Option (Lean.Expr × Lean.Expr))

Apply the result r for prop (which is inhabited by proof). Return none if the goal was closed. Return some (proof', prop') otherwise, where proof' : prop' and prop' is the simplified prop.

This method assumes mvarId is not assigned, and we are already using mvarIds local context.

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def Lean.Meta.applySimpResultToFVarId (mvarId : Lean.MVarId) (fvarId : Lean.FVarId) (r : Lean.Meta.Simp.Result) (mayCloseGoal : Bool) : Lean.MetaM (Option (Lean.Expr × Lean.Expr))

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def Lean.Meta.simpStep (mvarId : Lean.MVarId) (proof : Lean.Expr) (prop : Lean.Expr) (ctx : Lean.Meta.Simp.Context) (discharge? : optParam (Option Lean.Meta.Simp.Discharge) none) (mayCloseGoal : optParam Bool true) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Option (Lean.Expr × Lean.Expr) × Lean.Meta.Simp.UsedSimps)

Simplify prop (which is inhabited by proof). Return none if the goal was closed. Return some (proof', prop') otherwise, where proof' : prop' and prop' is the simplified prop.

This method assumes mvarId is not assigned, and we are already using mvarIds local context.

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def Lean.Meta.applySimpResultToLocalDeclCore (mvarId : Lean.MVarId) (fvarId : Lean.FVarId) (r : Option (Lean.Expr × Lean.Expr)) : Lean.MetaM (Option (Lean.FVarId × Lean.MVarId))

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def Lean.Meta.applySimpResultToLocalDecl (mvarId : Lean.MVarId) (fvarId : Lean.FVarId) (r : Lean.Meta.Simp.Result) (mayCloseGoal : Bool) : Lean.MetaM (Option (Lean.FVarId × Lean.MVarId))

Simplify simp result to the given local declaration. Return none if the goal was closed. This method assumes mvarId is not assigned, and we are already using mvarIds local context.

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def Lean.Meta.simpLocalDecl (mvarId : Lean.MVarId) (fvarId : Lean.FVarId) (ctx : Lean.Meta.Simp.Context) (discharge? : optParam (Option Lean.Meta.Simp.Discharge) none) (mayCloseGoal : optParam Bool true) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Option (Lean.FVarId × Lean.MVarId) × Lean.Meta.Simp.UsedSimps)

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def Lean.Meta.simpGoal (mvarId : Lean.MVarId) (ctx : Lean.Meta.Simp.Context) (discharge? : optParam (Option Lean.Meta.Simp.Discharge) none) (simplifyTarget : optParam Bool true) (fvarIdsToSimp : optParam (Array Lean.FVarId) #[]) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Option (Array Lean.FVarId × Lean.MVarId) × Lean.Meta.Simp.UsedSimps)

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def Lean.Meta.simpTargetStar (mvarId : Lean.MVarId) (ctx : Lean.Meta.Simp.Context) (discharge? : optParam (Option Lean.Meta.Simp.Discharge) none) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Lean.Meta.TacticResultCNM × Lean.Meta.Simp.UsedSimps)

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def Lean.Meta.dsimpGoal (mvarId : Lean.MVarId) (ctx : Lean.Meta.Simp.Context) (simplifyTarget : optParam Bool true) (fvarIdsToSimp : optParam (Array Lean.FVarId) #[]) (usedSimps : optParam Lean.Meta.Simp.UsedSimps ∅) : Lean.MetaM (Option Lean.MVarId × Lean.Meta.Simp.UsedSimps)

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