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fix: IsChain style improvements and deprecation correction #1663

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Merged
fgdorais merged 6 commits into from
Feb 13, 2026
Merged

fix: IsChain style improvements and deprecation correction #1663

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e45be82
IsChain style improvements
linesthatinterlace Feb 10, 2026
1a5dfa0
Remove trailing whitespace
linesthatinterlace Feb 10, 2026
e5014da
Merge branch 'main' into isChain_style
fgdorais Feb 12, 2026
7c2e4bd
Apply suggestions from code review
linesthatinterlace Feb 12, 2026
29fb405
Fix typo
linesthatinterlace Feb 12, 2026
f4e70b7
Improve proof
linesthatinterlace Feb 12, 2026
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20 changes: 11 additions & 9 deletions Batteries/Data/List/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -647,10 +647,12 @@ pwFilter (·<·) [0, 1, 5, 2, 6, 3, 4] = [0, 1, 2, 3, 4]
def pwFilter (R : α → α → Prop) [DecidableRel R] (l : List α) : List α :=
l.foldr (fun x IH => if ∀ y ∈ IH, R x y then x :: IH else IH) []

/-- `IsChain R l` means that `R` holds between adjacent elements of `l`.
/--
`IsChain R l` means that `R` holds between adjacent elements of `l`. Example:
```
IsChain R [a, b, c, d] ↔ R a b ∧ R b c ∧ R c d
``` -/
```
-/
inductive IsChain (R : α → α → Prop) : List α → Prop where
/-- A list of length 0 is a chain. -/
| nil : IsChain R []
Expand All @@ -665,13 +667,13 @@ attribute [simp, grind ←] IsChain.singleton
@[simp, grind =] theorem isChain_cons_cons : IsChain R (a :: b :: l) ↔ R a b ∧ IsChain R (b :: l) :=
⟨fun | .cons_cons hr h => ⟨hr, h⟩, fun ⟨hr, h⟩ => .cons_cons hr h⟩

instance instDecidableIsChain {R : α → α → Prop} [h : DecidableRel R] (l : List α) :
Decidable (l.IsChain R) := match l with | [] => isTrue .nil | a :: l => go a l
where
go (a : α) (l : List α) : Decidable ((a :: l).IsChain R) :=
match l with
| [] => isTrue <| .singleton a
| b :: l => haveI := (go b l); decidable_of_iff' _ isChain_cons_cons
instance {R : α → α → Prop} [h : DecidableRel R] : (l : List α) → Decidable (l.IsChain R)
| [] => isTrue .nil | a :: l => go a l
where
go (a : α) (l : List α) : Decidable ((a :: l).IsChain R) :=
match l with
| [] => isTrue <| .singleton a
| b :: l => haveI := (go b l); decidable_of_iff' _ isChain_cons_cons

/-- `Chain R a l` means that `R` holds between adjacent elements of `a::l`.
```
Expand Down
60 changes: 33 additions & 27 deletions Batteries/Data/List/Lemmas.lean
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Expand Up @@ -379,56 +379,62 @@ alias chain_cons := isChain_cons_cons
theorem rel_of_isChain_cons_cons (p : IsChain R (a :: b :: l)) : R a b :=
(isChain_cons_cons.1 p).1

alias IsChain.rel := rel_of_isChain_cons_cons

@[deprecated (since := "2025-09-19")]
alias rel_of_chain_cons := rel_of_isChain_cons_cons

theorem isChain_cons_of_isChain_cons_cons (p : IsChain R (a :: b :: l)) :
IsChain R (b :: l) := (isChain_cons_cons.1 p).2
theorem isChain_of_isChain_cons (p : IsChain R (b :: l)) : IsChain R l := by grind [cases List]

alias IsChain.of_cons := isChain_of_isChain_cons

@[deprecated IsChain.of_cons (since := "2026-02-10")]
theorem isChain_cons_of_isChain_cons_cons : IsChain R (a :: b :: l) →
IsChain R (b :: l) := IsChain.of_cons

@[deprecated (since := "2025-09-19")]
alias chain_of_chain_cons := isChain_cons_of_isChain_cons_cons

theorem isChain_of_isChain_cons (p : IsChain R (b :: l)) :
IsChain R l := by
cases l
· exact .nil
· exact isChain_cons_of_isChain_cons_cons p

theorem isChain_of_isChain_cons_cons (p : IsChain R (a :: b :: l)) :
IsChain R l := isChain_of_isChain_cons (isChain_of_isChain_cons p)
@[deprecated IsChain.of_cons (since := "2026-02-10")]
theorem isChain_of_isChain_cons_cons : IsChain R (a :: b :: l) →
IsChain R l := IsChain.of_cons ∘ IsChain.of_cons

@[grind =>]
theorem IsChain.imp (H : ∀ ⦃a b : α⦄, R a b → S a b)
(p : IsChain R l) : IsChain S l := by induction p with grind

@[deprecated (since := "2025-09-19")]
alias Chain.imp := IsChain.imp

theorem IsChain.cons_of_imp_of_cons (h : ∀ c, R a c → R b c) :
IsChain R (a :: l) → IsChain R (b :: l) := by cases l <;> grind
theorem IsChain.cons_of_imp (h : ∀ c, R a c → R b c) :
IsChain R (a :: l) → IsChain R (b :: l) := by grind [cases List]

@[deprecated IsChain.of_cons (since := "2026-02-10")]
alias IsChain.cons_of_imp_of_cons := IsChain.cons_of_imp

@[deprecated "Use IsChain.imp and IsChain.change_head" (since := "2025-09-19")]
theorem Chain.imp' (HRS : ∀ ⦃a b : α⦄, R a b → S a b)
(Hab : ∀ ⦃c⦄, R a c → S b c) : IsChain R (a :: l) → IsChain S (b :: l) := by
cases l with grind [IsChain.imp]
theorem IsChain.cons_of_imp_of_imp (HRS : ∀ ⦃a b : α⦄, R a b → S a b)
(Hab : ∀ ⦃c⦄, R a c → S b c) (h : IsChain R (a :: l)) : IsChain S (b :: l) := by
grind [cases List]

@[deprecated (since := "2025-09-19")]
alias Chain.imp' := IsChain.cons_of_imp_of_imp

@[deprecated (since := "2025-09-19")]
protected alias Pairwise.chain := Pairwise.isChain

@[grind →] protected theorem IsChain.pairwise [Trans R R R] (c : IsChain R l) :
Pairwise R l := by
induction c with
| nil | singleton => grind
| cons_cons hr h p =>
simp only [pairwise_cons, mem_cons, forall_eq_or_imp] at p ⊢
exact ⟨⟨hr, fun _ ha => Trans.trans hr <| p.1 _ ha⟩, p⟩
theorem isChain_iff_pairwise [Trans R R R] : IsChain R l ↔ Pairwise R l := by
induction l with | nil => grind | cons a l IH => cases l with | nil => grind | cons b l =>
simp only [isChain_cons_cons, IH, pairwise_cons, mem_cons, forall_eq_or_imp, and_congr_left_iff,
iff_self_and, and_imp]
exact flip <| fun _ => flip (Trans.trans · <| · · ·)

theorem isChain_iff_pairwise [Trans R R R] : IsChain R l ↔ Pairwise R l := by grind
@[grind →] protected theorem IsChain.pairwise [Trans R R R] (c : IsChain R l) :
Pairwise R l := isChain_iff_pairwise.mp c

theorem isChain_iff_getElem {l : List α} :
IsChain R l ↔ ∀ (i : Nat) (_hi : i + 1 < l.length), R l[i] l[i + 1] := by
induction l with
| nil => grind
| cons a l IH => cases l with | nil => grind | cons b l => simp [IH, Nat.forall_lt_succ_left']
induction l with | nil => grind | cons a l IH => cases l with | nil => grind | cons b l =>
simp [IH, Nat.forall_lt_succ_left']

theorem IsChain.getElem {l : List α} (c : IsChain R l) (i : Nat) (hi : i + 1 < l.length) :
R l[i] l[i + 1] := isChain_iff_getElem.mp c _ _
Expand Down