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def Tactic.NormCast.proveEqUsing (s : Lean.Meta.SimpTheorems) (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM (Option Lean.Meta.Simp.Result)

Prove a = b using the given simp set.

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def Tactic.NormCast.proveEqUsingDown (a : Lean.Expr) (b : Lean.Expr) : Lean.MetaM (Option Lean.Meta.Simp.Result)

Prove a = b by simplifying using move and squash lemmas.

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def Tactic.NormCast.mkCoe (e : Lean.Expr) (ty : Lean.Expr) : Lean.MetaM Lean.Expr

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• Tactic.NormCast.mkCoe e ty = do let __discr ← Lean.Meta.coerce? e ty match __discr with | Lean.LOption.some e' => pure e' | x => failure

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def Tactic.NormCast.isCoeOf? (e : Lean.Expr) : Lean.MetaM (Option Lean.Expr)

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def Tactic.NormCast.isNumeral? (e : Lean.Expr) : Option (Lean.Expr × ℕ)

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def Tactic.NormCast.splittingProcedure (expr : Lean.Expr) : Lean.MetaM Lean.Meta.Simp.Result

This is the main heuristic used alongside the elim and move lemmas. The goal is to help casts move past operators by adding intermediate casts. An expression of the shape: op (↑(x : α) : γ) (↑(y : β) : γ) is rewritten to: op (↑(↑(x : α) : β) : γ) (↑(y : β) : γ) when (↑(↑(x : α) : β) : γ) = (↑(x : α) : γ) can be proven with a squash lemma

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def Tactic.NormCast.prove (e : Lean.Expr) : Lean.Meta.SimpM (Option Lean.Expr)

Discharging function used during simplification in the "squash" step.

TODO: normCast takes a list of expressions to use as lemmas for the discharger TODO: a tactic to print the results the discharger fails to proove

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def Tactic.NormCast.upwardAndElim (up : Lean.Meta.SimpTheorems) (e : Lean.Expr) : Lean.Meta.SimpM Lean.Meta.Simp.Step

Core rewriting function used in the "squash" step, which moves casts upwards and eliminates them.

It tries to rewrite an expression using the elim and move lemmas. On failure, it calls the splitting procedure heuristic.

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def Tactic.NormCast.numeralToCoe (e : Lean.Expr) : Lean.MetaM Lean.Meta.Simp.Result

If possible, rewrite (n : α) to (Nat.cast n : α) where n is a numeral and α ≠ ℕ. Returns a pair of the new expression and proof that they are equal.

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def Tactic.NormCast.derive (e : Lean.Expr) : Lean.MetaM Lean.Meta.Simp.Result

The core simplification routine of normCast.

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def Tactic.NormCast.termMod_cast_ : Lean.ParserDescr

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def Tactic.NormCast.normCastTarget : Lean.Elab.Tactic.TacticM Unit

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def Tactic.NormCast.normCastHyp (fvarId : Lean.FVarId) : Lean.Elab.Tactic.TacticM Unit

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def Tactic.NormCast.tacticNorm_cast0__ : Lean.ParserDescr

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def Tactic.NormCast.tacticAssumption_mod_cast : Lean.ParserDescr

assumption_mod_cast runs norm_cast on the goal. For each local hypothesis h, it also normalizes h and tries to use that to close the goal.

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• Tactic.NormCast.tacticAssumption_mod_cast = Lean.ParserDescr.node `Tactic.NormCast.tacticAssumption_mod_cast 1024 (Lean.ParserDescr.nonReservedSymbol "assumption_mod_cast" false)

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def Tactic.NormCast.tacticNorm_cast__ : Lean.ParserDescr

Normalize casts at the given locations by moving them "upwards".

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def Tactic.NormCast.tacticRw_mod_cast____ : Lean.ParserDescr

Rewrite with the given rules and normalize casts between steps.

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def Tactic.NormCast.tacticExact_mod_cast_ : Lean.ParserDescr

Normalize the goal and the given expression, then close the goal with exact.

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def Tactic.NormCast.tacticApply_mod_cast_ : Lean.ParserDescr

Normalize the goal and the given expression, then apply the expression to the goal.

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def Tactic.NormCast.convNormCast : Lean.ParserDescr

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• Tactic.NormCast.convNormCast = Lean.ParserDescr.node `Tactic.NormCast.convNormCast 1024 (Lean.ParserDescr.nonReservedSymbol "norm_cast" false)

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def Tactic.NormCast.evalConvNormCast : Lean.Elab.Tactic.Tactic

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def Tactic.NormCast.pushCast : Lean.ParserDescr

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def Tactic.NormCast.evalPushCast : Lean.Elab.Tactic.Tactic

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