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.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.instInhabitedSimpM {α : Type} : Inhabited (Lean.Meta.SimpM α)

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• Lean.Meta.Simp.instInhabitedSimpM = { default := fun (x : Lean.Meta.Simp.MethodsRef) (x : Lean.Meta.Simp.Context) (x : ST.Ref IO.RealWorld Lean.Meta.Simp.State) => default }

def Lean.Meta.Simp.lambdaTelescopeDSimp {α : Type} (e : Lean.Expr) (k : Array Lean.Expr → Lean.Expr → Lean.Meta.SimpM α) : Lean.Meta.SimpM 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.SimpM α) (xs : Array Lean.Expr) (e : Lean.Expr) : Lean.Meta.SimpM 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 : Lake.Name) (t : Lean.Expr) (b : Lean.Expr) : Lean.MetaM Lean.Meta.Simp.SimpLetCase

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

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

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def Lean.Meta.Simp.simpProj (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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

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

def Lean.Meta.Simp.simpLambda (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.simpArrow (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.simpForall (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.simpLet (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.visitFn (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.congrDefault (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.processCongrHypothesis (h : Lean.Expr) : Lean.Meta.SimpM Bool

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

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

Try to rewrite e children using the given congruence theorem

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def Lean.Meta.Simp.congr (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.simpApp (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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• Lean.Meta.Simp.simpApp e = if Lean.Meta.Simp.isOfNatNatLit e = true then pure { expr := e, proof? := none, dischargeDepth := 0, cache := true } else Lean.Meta.Simp.congr e

def Lean.Meta.Simp.simpStep (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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

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partial def Lean.Meta.Simp.simpLoop (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simpLoop.visitPreContinue (e : Lean.Expr) (cfg : Lean.Meta.Simp.Config) (r : Lean.Meta.Simp.Result) : Lean.Meta.SimpM Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simpLoop.visitPost (e : Lean.Expr) (cfg : Lean.Meta.Simp.Config) (r : Lean.Meta.Simp.Result) : Lean.Meta.SimpM Lean.Meta.Simp.Result

partial def Lean.Meta.Simp.simpLoop.visitPostContinue (e : Lean.Expr) (cfg : Lean.Meta.Simp.Config) (r : Lean.Meta.Simp.Result) : Lean.Meta.SimpM Lean.Meta.Simp.Result

@[export lean_simp]

def Lean.Meta.Simp.simpImpl (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Result

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def Lean.Meta.Simp.simpImpl.go (e : Lean.Expr) : Lean.Meta.SimpM 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 (x : Lean.Expr) => pure Lean.Meta.Simp.Step.continue, post := fun (e : Lean.Expr) => pure (Lean.Meta.Simp.Step.done { expr := e, proof? := none, dischargeDepth := 0, cache := true }), discharge? := fun (x : Lean.Expr) => 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 (x : Lean.Expr) => pure Lean.Meta.Simp.Step.continue, post := fun (e : Lean.Expr) => pure (Lean.Meta.Simp.Step.done { expr := e, proof? := none, dischargeDepth := 0, cache := true }), discharge? := fun (x : Lean.Expr) => pure none }) : Lean.MetaM (Lean.Expr × Lean.Meta.Simp.UsedSimps)

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def Lean.Meta.simp (e : Lean.Expr) (ctx : Lean.Meta.Simp.Context) (simprocs : optParam Lean.Meta.Simp.SimprocsArray #[]) (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.simpTargetCore (mvarId : Lean.MVarId) (ctx : Lean.Meta.Simp.Context) (simprocs : optParam Lean.Meta.Simp.SimprocsArray #[]) (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) (simprocs : optParam Lean.Meta.Simp.SimprocsArray #[]) (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) (simprocs : optParam Lean.Meta.Simp.SimprocsArray #[]) (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) (simprocs : optParam Lean.Meta.Simp.SimprocsArray #[]) (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) (simprocs : optParam Lean.Meta.Simp.SimprocsArray #[]) (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) (simprocs : optParam Lean.Meta.Simp.SimprocsArray #[]) (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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