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feat: Rxx.nodup_toList lemmas and slice/foldl lemmas #12438

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datokrat merged 3 commits into from
Feb 16, 2026
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feat: Rxx.nodup_toList lemmas and slice/foldl lemmas #12438

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TreeSet.mem_toList: grind =
datokrat Feb 11, 2026
495a4c8
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datokrat Feb 11, 2026
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fix
datokrat Feb 11, 2026
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80 changes: 80 additions & 0 deletions src/Init/Data/Range/Polymorphic/Lemmas.lean
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Expand Up @@ -535,6 +535,14 @@ public theorem Rxc.Iterator.pairwise_toList_upwardEnumerableLt [LE α] [Decidabl
· apply ihy (out := a)
simp_all [Rxc.Iterator.isPlausibleStep_iff, Rxc.Iterator.step]

theorem Rxc.Iterator.nodup_toList [LE α] [DecidableLE α]
[PRange.UpwardEnumerable α] [Rxc.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
[PRange.LawfulUpwardEnumerableLE α]
{it : Iter (α := Rxc.Iterator α) α} :
it.toList.Nodup := by
apply (Rxc.Iterator.pairwise_toList_upwardEnumerableLt it).imp
apply PRange.UpwardEnumerable.ne_of_lt

public theorem Rxo.Iterator.pairwise_toList_upwardEnumerableLt [LT α] [DecidableLT α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLT α]
[Rxo.IsAlwaysFinite α]
Expand All @@ -558,6 +566,14 @@ public theorem Rxo.Iterator.pairwise_toList_upwardEnumerableLt [LT α] [Decidabl
· apply ihy (out := a)
simp_all [Rxo.Iterator.isPlausibleStep_iff, Rxo.Iterator.step]

theorem Rxo.Iterator.nodup_toList [LT α] [DecidableLT α]
[PRange.UpwardEnumerable α] [Rxo.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
[PRange.LawfulUpwardEnumerableLT α]
{it : Iter (α := Rxo.Iterator α) α} :
it.toList.Nodup := by
apply (Rxo.Iterator.pairwise_toList_upwardEnumerableLt it).imp
apply PRange.UpwardEnumerable.ne_of_lt

public theorem Rxi.Iterator.pairwise_toList_upwardEnumerableLt
[UpwardEnumerable α] [LawfulUpwardEnumerable α]
[Rxi.IsAlwaysFinite α]
Expand All @@ -581,6 +597,13 @@ public theorem Rxi.Iterator.pairwise_toList_upwardEnumerableLt
· apply ihy (out := a)
simp_all [Rxi.Iterator.isPlausibleStep_iff, Rxi.Iterator.step]

theorem Rxi.Iterator.nodup_toList
[PRange.UpwardEnumerable α] [Rxi.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
{it : Iter (α := Rxi.Iterator α) α} :
it.toList.Nodup := by
apply (Rxi.Iterator.pairwise_toList_upwardEnumerableLt it).imp
apply PRange.UpwardEnumerable.ne_of_lt

namespace Rcc

variable {r : Rcc α}
Expand Down Expand Up @@ -658,6 +681,13 @@ public theorem pairwise_toList_upwardEnumerableLt [LE α] [DecidableLE α]
rw [Internal.toList_eq_toList_iter]
apply Rxc.Iterator.pairwise_toList_upwardEnumerableLt

public theorem nodup_toList [LE α] [DecidableLE α]
[PRange.UpwardEnumerable α] [Rxc.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
[PRange.LawfulUpwardEnumerableLE α]
{a b : α} :
(a...=b).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxc.Iterator.nodup_toList

public theorem pairwise_toList_ne [LE α] [DecidableLE α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLE α]
[Rxc.IsAlwaysFinite α] :
Expand Down Expand Up @@ -913,6 +943,13 @@ public theorem pairwise_toList_upwardEnumerableLt [LE α] [LT α] [DecidableLT
rw [Internal.toList_eq_toList_iter]
apply Rxo.Iterator.pairwise_toList_upwardEnumerableLt

public theorem nodup_toList [LT α] [DecidableLT α]
[PRange.UpwardEnumerable α] [Rxo.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
[PRange.LawfulUpwardEnumerableLT α]
{a b : α} :
(a...b).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxo.Iterator.nodup_toList

public theorem pairwise_toList_ne [LE α] [LT α] [DecidableLT α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLT α]
[Rxo.IsAlwaysFinite α] :
Expand Down Expand Up @@ -1124,6 +1161,11 @@ public theorem pairwise_toList_upwardEnumerableLt [LE α]
rw [Internal.toList_eq_toList_iter]
apply Rxi.Iterator.pairwise_toList_upwardEnumerableLt

public theorem nodup_toList
[PRange.UpwardEnumerable α] [Rxi.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
{a : α} : (a...*).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxi.Iterator.nodup_toList

public theorem pairwise_toList_ne [LE α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [Rxi.IsAlwaysFinite α] :
r.toList.Pairwise (fun a b => a ≠ b) :=
Expand Down Expand Up @@ -1363,6 +1405,13 @@ public theorem pairwise_toList_upwardEnumerableLt [LE α] [DecidableLE α]
rw [Internal.toList_eq_toList_iter]
apply Rxc.Iterator.pairwise_toList_upwardEnumerableLt

public theorem nodup_toList [LE α] [DecidableLE α]
[PRange.UpwardEnumerable α] [Rxc.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
[PRange.LawfulUpwardEnumerableLE α]
{a b : α} :
(a<...=b).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxc.Iterator.nodup_toList

public theorem pairwise_toList_ne [LE α] [DecidableLE α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLE α]
[Rxc.IsAlwaysFinite α] :
Expand Down Expand Up @@ -1588,6 +1637,13 @@ public theorem pairwise_toList_upwardEnumerableLt [LT α] [DecidableLT α]
rw [Internal.toList_eq_toList_iter]
apply Rxo.Iterator.pairwise_toList_upwardEnumerableLt

public theorem nodup_toList [LT α] [DecidableLT α]
[PRange.UpwardEnumerable α] [Rxo.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
[PRange.LawfulUpwardEnumerableLT α]
{a b : α} :
(a<...b).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxo.Iterator.nodup_toList

public theorem pairwise_toList_ne [LT α] [DecidableLT α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLT α]
[Rxo.IsAlwaysFinite α] :
Expand Down Expand Up @@ -1823,6 +1879,11 @@ public theorem pairwise_toList_upwardEnumerableLt
rw [Internal.toList_eq_toList_iter]
apply Rxi.Iterator.pairwise_toList_upwardEnumerableLt

public theorem nodup_toList
[PRange.UpwardEnumerable α] [Rxi.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
{a : α} : (a<...*).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxi.Iterator.nodup_toList

public theorem pairwise_toList_ne
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [Rxi.IsAlwaysFinite α] :
r.toList.Pairwise (fun a b => a ≠ b) :=
Expand Down Expand Up @@ -2072,6 +2133,13 @@ public theorem pairwise_toList_upwardEnumerableLt [LE α] [DecidableLE α] [Leas
r.toList.Pairwise (fun a b => UpwardEnumerable.LT a b) := by
simp [toList_eq_toList_rcc, Rcc.pairwise_toList_upwardEnumerableLt]

public theorem nodup_toList [LE α] [DecidableLE α] [Least? α]
[PRange.UpwardEnumerable α] [Rxc.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
[PRange.LawfulUpwardEnumerableLE α]
{a : α} :
(*...=a).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxc.Iterator.nodup_toList

public theorem pairwise_toList_ne [LE α] [DecidableLE α] [Least? α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLE α]
[LawfulUpwardEnumerableLeast? α] [Rxc.IsAlwaysFinite α] :
Expand Down Expand Up @@ -2395,6 +2463,13 @@ public theorem pairwise_toList_upwardEnumerableLt [LT α] [DecidableLT α] [Leas
· exact Roo.pairwise_toList_upwardEnumerableLt
· simp

public theorem nodup_toList [LT α] [DecidableLT α] [Least? α]
[PRange.UpwardEnumerable α] [Rxo.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α]
[PRange.LawfulUpwardEnumerableLT α]
{a : α} :
(*...a).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxo.Iterator.nodup_toList

public theorem pairwise_toList_ne [LT α] [DecidableLT α] [Least? α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLT α]
[LawfulUpwardEnumerableLeast? α] [Rxo.IsAlwaysFinite α] :
Expand Down Expand Up @@ -2688,6 +2763,11 @@ public theorem pairwise_toList_upwardEnumerableLt [Least? α]
· simp
· exact Rci.pairwise_toList_upwardEnumerableLt

public theorem nodup_toList [Least? α]
[PRange.UpwardEnumerable α] [Rxi.IsAlwaysFinite α] [PRange.LawfulUpwardEnumerable α] :
(*...* : Std.Rii α).toList.Nodup := by
simpa [Internal.toList_eq_toList_iter] using Std.Rxi.Iterator.nodup_toList

public theorem pairwise_toList_ne [Least? α]
[UpwardEnumerable α] [LawfulUpwardEnumerable α]
[LawfulUpwardEnumerableLeast? α] [Rxi.IsAlwaysFinite α] :
Expand Down
6 changes: 3 additions & 3 deletions src/Init/Data/Slice/Array/Lemmas.lean
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Expand Up @@ -100,11 +100,11 @@ end SubarrayIterator

namespace Subarray

theorem internalIter_eq {α : Type u} {s : Subarray α} :
theorem Internal.iter_eq {α : Type u} {s : Subarray α} :
Internal.iter s = ⟨⟨s⟩⟩ :=
rfl

theorem toList_internalIter {α : Type u} {s : Subarray α} :
theorem Internal.toList_iter {α : Type u} {s : Subarray α} :
(Internal.iter s).toList =
(s.array.toList.take s.stop).drop s.start := by
simp [SubarrayIterator.toList_eq, Internal.iter_eq_toIteratorIter, ToIterator.iter_eq]
Expand Down Expand Up @@ -223,7 +223,7 @@ public theorem Subarray.toList_eq {xs : Subarray α} :
change aslice.toList = _
have : aslice.toList = lslice.toList := by
rw [ListSlice.toList_eq]
simp +instances only [aslice, lslice, Std.Slice.toList, toList_internalIter]
simp +instances only [aslice, lslice, Std.Slice.toList, Internal.toList_iter]
apply List.ext_getElem
· have : stop - start ≤ array.size - start := by omega
simp [Subarray.start, Subarray.stop, *, Subarray.array]
Expand Down
20 changes: 9 additions & 11 deletions src/Init/Data/Slice/InternalLemmas.lean
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Expand Up @@ -25,47 +25,45 @@ theorem Internal.iter_eq_toIteratorIter {γ : Type u}
Internal.iter s = ToIterator.iter s :=
(rfl)

theorem forIn_internalIter {γ : Type u} {β : Type v}
theorem Internal.forIn_iter {γ : Type u} {β : Type v}
{m : Type w → Type x} [Monad m] {δ : Type w}
[ToIterator (Slice γ) Id α β]
[Iterator α Id β]
[IteratorLoop α Id m]
[LawfulIteratorLoop α Id m]
[Finite α Id] {s : Slice γ}
[Iterator α Id β] [IteratorLoop α Id m]
{s : Slice γ}
{init : δ} {f : β → δ → m (ForInStep δ)} :
ForIn.forIn (Internal.iter s) init f = ForIn.forIn s init f :=
(rfl)

theorem Internal.size_eq_length_internalIter [ToIterator (Slice γ) Id α β]
theorem Internal.size_eq_length_iter [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [Finite α Id]
[IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
{s : Slice γ} [SliceSize γ] [LawfulSliceSize γ] :
s.size = (Internal.iter s).length := by
simp only [Slice.size, iter, LawfulSliceSize.lawful, ← Iter.length_toList_eq_length]

theorem Internal.toArray_eq_toArray_internalIter {s : Slice γ} [ToIterator (Slice γ) Id α β]
theorem Internal.toArray_eq_toArray_iter {s : Slice γ} [ToIterator (Slice γ) Id α β]
[Iterator α Id β]
[Finite α Id] :
s.toArray = (Internal.iter s).toArray :=
(rfl)

theorem Internal.toList_eq_toList_internalIter {s : Slice γ} [ToIterator (Slice γ) Id α β]
theorem Internal.toList_eq_toList_iter {s : Slice γ} [ToIterator (Slice γ) Id α β]
[Iterator α Id β]
[Finite α Id] :
s.toList = (Internal.iter s).toList :=
(rfl)

theorem Internal.toListRev_eq_toListRev_internalIter {s : Slice γ} [ToIterator (Slice γ) Id α β]
theorem Internal.toListRev_eq_toListRev_iter {s : Slice γ} [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [Finite α Id] :
s.toListRev = (Internal.iter s).toListRev :=
(rfl)

theorem fold_internalIter [ToIterator (Slice γ) Id α β]
theorem Internal.fold_iter [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id Id] [Iterators.Finite α Id] {s : Slice γ} :
(Internal.iter s).fold (init := init) f = s.foldl (init := init) f := by
rfl

theorem foldM_internalIter {m : Type w → Type w'} [Monad m] [ToIterator (Slice γ) Id α β]
theorem Internal.foldM_iter {m : Type w → Type w'} [Monad m] [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id m] [Iterators.Finite α Id] {s : Slice γ} {f : δ → β → m δ} :
(Internal.iter s).foldM (init := init) f = s.foldlM (init := init) f := by
rfl
71 changes: 48 additions & 23 deletions src/Init/Data/Slice/Lemmas.lean
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Expand Up @@ -11,17 +11,18 @@ import all Init.Data.Slice.Operations
import Init.Data.Iterators.Lemmas.Consumers
public import Init.Data.List.Control
public import Init.Data.Iterators.Consumers.Collect

import Init.Data.Slice.InternalLemmas

public section

open Std Std.Iterators

namespace Std.Slice

variable {γ : Type u} {α β : Type v}

@[simp]
public theorem forIn_toList {γ : Type u} {β : Type v}
theorem forIn_toList {γ : Type u} {β : Type v}
{m : Type w → Type x} [Monad m] [LawfulMonad m] {δ : Type w}
[ToIterator (Slice γ) Id α β]
[Iterator α Id β]
Expand All @@ -30,10 +31,10 @@ public theorem forIn_toList {γ : Type u} {β : Type v}
[Finite α Id] {s : Slice γ}
{init : δ} {f : β → δ → m (ForInStep δ)} :
ForIn.forIn s.toList init f = ForIn.forIn s init f := by
rw [← forIn_internalIter, ← Iter.forIn_toList, Slice.toList]
rw [← Internal.forIn_iter, ← Iter.forIn_toList, Slice.toList]

@[simp]
public theorem forIn_toArray {γ : Type u} {β : Type v}
theorem forIn_toArray {γ : Type u} {β : Type v}
{m : Type w → Type x} [Monad m] [LawfulMonad m] {δ : Type w}
[ToIterator (Slice γ) Id α β]
[Iterator α Id β]
Expand All @@ -42,46 +43,70 @@ public theorem forIn_toArray {γ : Type u} {β : Type v}
[Finite α Id] {s : Slice γ}
{init : δ} {f : β → δ → m (ForInStep δ)} :
ForIn.forIn s.toArray init f = ForIn.forIn s init f := by
rw [← forIn_internalIter, ← Iter.forIn_toArray, Slice.toArray]
rw [← Internal.forIn_iter, ← Iter.forIn_toArray, Slice.toArray]

theorem Internal.foldlM_iter [Monad m] [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id m]
{s : Slice γ} {init : δ} {f : δ → β → m δ} :
(Internal.iter s).foldM (init := init) f = s.foldlM (init := init) f :=
(rfl)

theorem foldlM_toList [Monad m] [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
[Finite α Id] [LawfulMonad m] {s : Slice γ} {init : δ} {f : δ → β → m δ} :
s.toList.foldlM (init := init) f = s.foldlM (init := init) f := by
simp [← Internal.foldlM_iter, ← Iter.foldlM_toList, Slice.toList]

theorem foldlM_toArray [Monad m] [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
[Finite α Id] [LawfulMonad m] {s : Slice γ} {init : δ} {f : δ → β → m δ} :
s.toArray.foldlM (init := init) f = s.foldlM (init := init) f := by
simp [← Internal.foldlM_iter, ← Iter.foldlM_toArray, Slice.toArray]

theorem Internal.foldl_iter [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id Id]
{s : Slice γ} {init : δ} {f : δ → β → δ} :
(Internal.iter s).fold (init := init) f = s.foldl (init := init) f :=
(rfl)

theorem foldl_toList [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
[Finite α Id] {s : Slice γ} {init : δ} {f : δ → β → δ} :
s.toList.foldl (init := init) f = s.foldl (init := init) f := by
simp [← Internal.foldl_iter, ← Iter.foldl_toList, Slice.toList]

theorem foldl_toArray [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
[Finite α Id] {s : Slice γ} {init : δ} {f : δ → β → δ} :
s.toArray.foldl (init := init) f = s.foldl (init := init) f := by
simp [← Internal.foldl_iter, ← Iter.foldl_toArray, Slice.toArray]

@[simp, grind =, suggest_for ListSlice.size_toArray ListSlice.size_toArray_eq_size]
public theorem size_toArray_eq_size [ToIterator (Slice γ) Id α β]
theorem size_toArray_eq_size [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [SliceSize γ] [LawfulSliceSize γ]
[Finite α Id]
{s : Slice γ} :
s.toArray.size = s.size := by
letI : IteratorLoop α Id Id := .defaultImplementation
rw [Internal.size_eq_length_internalIter, Internal.toArray_eq_toArray_internalIter, Iter.size_toArray_eq_length]
rw [Internal.size_eq_length_iter, Internal.toArray_eq_toArray_iter, Iter.size_toArray_eq_length]

@[simp, grind =, suggest_for ListSlice.length_toList ListSlice.length_toList_eq_size]
public theorem length_toList_eq_size [ToIterator (Slice γ) Id α β]
theorem length_toList_eq_size [ToIterator (Slice γ) Id α β]
[Iterator α Id β] {s : Slice γ}
[SliceSize γ] [LawfulSliceSize γ]
[Finite α Id] :
s.toList.length = s.size := by
letI : IteratorLoop α Id Id := .defaultImplementation
rw [Internal.size_eq_length_internalIter, Internal.toList_eq_toList_internalIter, Iter.length_toList_eq_length]
rw [Internal.size_eq_length_iter, Internal.toList_eq_toList_iter, Iter.length_toList_eq_length]

@[simp, grind =]
public theorem length_toListRev_eq_size [ToIterator (Slice γ) Id α β]
theorem length_toListRev_eq_size [ToIterator (Slice γ) Id α β]
[Iterator α Id β] {s : Slice γ}
[IteratorLoop α Id Id.{v}] [SliceSize γ] [LawfulSliceSize γ]
[Finite α Id]
[LawfulIteratorLoop α Id Id] :
s.toListRev.length = s.size := by
rw [Internal.size_eq_length_internalIter, Internal.toListRev_eq_toListRev_internalIter,
rw [Internal.size_eq_length_iter, Internal.toListRev_eq_toListRev_iter,
Iter.length_toListRev_eq_length]

public theorem foldlM_toList {m} [Monad m] [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [LawfulMonad m] [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
[Iterators.Finite α Id] {s : Slice γ} {f} :
s.toList.foldlM (init := init) f = s.foldlM (m := m) (init := init) f := by
simp [Internal.toList_eq_toList_internalIter, Iter.foldlM_toList, foldM_internalIter]

public theorem foldl_toList [ToIterator (Slice γ) Id α β]
[Iterator α Id β] [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
[Iterators.Finite α Id] {s : Slice γ} :
s.toList.foldl (init := init) f = s.foldl (init := init) f := by
simp [Internal.toList_eq_toList_internalIter, Iter.foldl_toList, fold_internalIter]

end Std.Slice
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