chore: cleanup of @[grind] lemmas for Option (#8217)
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Kim Morrison
GitHub
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3 changed files with 52 additions and 34 deletions
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@ -91,8 +91,6 @@ theorem eq_some_unique {o : Option α} {a b : α} (ha : o = some a) (hb : o = so
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| some _, _, H => ((H _).1 rfl).symm
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| _, some _, H => (H _).2 rfl
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set_option Elab.async false
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theorem eq_none_iff_forall_ne_some : o = none ↔ ∀ a, o ≠ some a := by
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cases o <;> simp
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@ -174,13 +172,13 @@ theorem forall_ne_none {p : Option α → Prop} : (∀ x (_ : x ≠ none), p x)
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@[deprecated forall_ne_none (since := "2025-04-04")]
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abbrev ball_ne_none := @forall_ne_none
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@[simp] theorem pure_def : pure = @some α := rfl
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@[simp, grind] theorem pure_def : pure = @some α := rfl
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@[simp] theorem bind_eq_bind : bind = @Option.bind α β := rfl
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@[simp, grind] theorem bind_eq_bind : bind = @Option.bind α β := rfl
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@[simp] theorem orElse_eq_orElse : HOrElse.hOrElse = @Option.orElse α := rfl
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@[simp, grind] theorem orElse_eq_orElse : HOrElse.hOrElse = @Option.orElse α := rfl
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@[simp] theorem bind_fun_some (x : Option α) : x.bind some = x := by cases x <;> rfl
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@[simp, grind] theorem bind_fun_some (x : Option α) : x.bind some = x := by cases x <;> rfl
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@[simp] theorem bind_fun_none (x : Option α) : x.bind (fun _ => none (α := β)) = none := by
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cases x <;> rfl
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@ -201,7 +199,7 @@ theorem bind_eq_none' {o : Option α} {f : α → Option β} :
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o.bind f = none ↔ ∀ b a, o = some a → f a ≠ some b := by
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cases o <;> simp [eq_none_iff_forall_ne_some]
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theorem mem_bind_iff {o : Option α} {f : α → Option β} :
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@[grind] theorem mem_bind_iff {o : Option α} {f : α → Option β} :
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b ∈ o.bind f ↔ ∃ a, a ∈ o ∧ b ∈ f a := by
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cases o <;> simp
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@ -209,6 +207,7 @@ theorem bind_comm {f : α → β → Option γ} (a : Option α) (b : Option β)
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(a.bind fun x => b.bind (f x)) = b.bind fun y => a.bind fun x => f x y := by
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cases a <;> cases b <;> rfl
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@[grind]
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theorem bind_assoc (x : Option α) (f : α → Option β) (g : β → Option γ) :
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(x.bind f).bind g = x.bind fun y => (f y).bind g := by cases x <;> rfl
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@ -216,10 +215,16 @@ theorem bind_congr {α β} {o : Option α} {f g : α → Option β} :
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(h : ∀ a, o = some a → f a = g a) → o.bind f = o.bind g := by
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cases o <;> simp
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@[grind]
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theorem isSome_bind {α β : Type _} (x : Option α) (f : α → Option β) :
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(x.bind f).isSome = x.any (fun x => (f x).isSome) := by
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cases x <;> rfl
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@[grind]
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theorem isNone_bind {α β : Type _} (x : Option α) (f : α → Option β) :
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(x.bind f).isNone = x.all (fun x => (f x).isNone) := by
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cases x <;> rfl
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theorem isSome_of_isSome_bind {α β : Type _} {x : Option α} {f : α → Option β}
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(h : (x.bind f).isSome) : x.isSome := by
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cases x <;> trivial
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@ -228,7 +233,7 @@ theorem isSome_apply_of_isSome_bind {α β : Type _} {x : Option α} {f : α →
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(h : (x.bind f).isSome) : (f (x.get (isSome_of_isSome_bind h))).isSome := by
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cases x <;> trivial
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@[simp] theorem get_bind {α β : Type _} {x : Option α} {f : α → Option β} (h : (x.bind f).isSome) :
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@[simp, grind] theorem get_bind {α β : Type _} {x : Option α} {f : α → Option β} (h : (x.bind f).isSome) :
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(x.bind f).get h = (f (x.get (isSome_of_isSome_bind h))).get
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(isSome_apply_of_isSome_bind h) := by
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cases x <;> trivial
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@ -251,9 +256,9 @@ theorem join_eq_none_iff : o.join = none ↔ o = none ∨ o = some none :=
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@[deprecated join_eq_none_iff (since := "2025-04-10")]
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abbrev join_eq_none := @join_eq_none_iff
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theorem bind_id_eq_join {x : Option (Option α)} : x.bind id = x.join := rfl
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@[grind] theorem bind_id_eq_join {x : Option (Option α)} : x.bind id = x.join := rfl
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@[simp] theorem map_eq_map : Functor.map f = Option.map f := rfl
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@[simp, grind] theorem map_eq_map : Functor.map f = Option.map f := rfl
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@[deprecated map_none (since := "2025-04-10")]
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abbrev map_none' := @map_none
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@ -316,7 +321,7 @@ theorem map_id' {x : Option α} : (x.map fun a => a) = x := congrFun map_id x
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theorem comp_map (h : β → γ) (g : α → β) (x : Option α) : x.map (h ∘ g) = (x.map g).map h :=
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(map_map ..).symm
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@[simp] theorem map_comp_map (f : α → β) (g : β → γ) :
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@[simp, grind _=_] theorem map_comp_map (f : α → β) (g : β → γ) :
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Option.map g ∘ Option.map f = Option.map (g ∘ f) := by funext x; simp
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theorem mem_map_of_mem (g : α → β) (h : a ∈ x) : g a ∈ Option.map g x := h.symm ▸ map_some ..
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@ -373,6 +378,7 @@ abbrev filter_eq_none := @filter_eq_none_iff
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@[deprecated filter_eq_some_iff (since := "2025-04-10")]
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abbrev filter_eq_some := @filter_eq_some_iff
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@[grind]
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theorem mem_filter_iff {p : α → Bool} {a : α} {o : Option α} :
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a ∈ o.filter p ↔ a ∈ o ∧ p a := by
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simp
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@ -425,10 +431,16 @@ theorem any_eq_false_iff_get (p : α → Bool) (x : Option α) :
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theorem isSome_of_any {x : Option α} {p : α → Bool} (h : x.any p) : x.isSome := by
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cases x <;> trivial
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@[grind]
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theorem any_map {α β : Type _} {x : Option α} {f : α → β} {p : β → Bool} :
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(x.map f).any p = x.any (fun a => p (f a)) := by
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cases x <;> rfl
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@[grind]
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theorem all_map {α β : Type _} {x : Option α} {f : α → β} {p : β → Bool} :
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(x.map f).all p = x.all (fun a => p (f a)) := by
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cases x <;> rfl
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theorem bind_map_comm {α β} {x : Option (Option α)} {f : α → β} :
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x.bind (Option.map f) = (x.map (Option.map f)).bind id := by cases x <;> simp
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@ -462,7 +474,7 @@ theorem orElse_eq_some_iff (o : Option α) (f) (x : α) :
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theorem orElse_eq_none_iff (o : Option α) (f) : (o.orElse f) = none ↔ o = none ∧ f () = none := by
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cases o <;> simp
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@[grind]theorem map_orElse {x : Option α} {y} :
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@[grind] theorem map_orElse {x : Option α} {y} :
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(x.orElse y).map f = (x.map f).orElse (fun _ => (y ()).map f) := by
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cases x <;> simp
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@ -515,6 +527,7 @@ theorem guard_eq_map (p : α → Bool) :
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funext x
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simp [Option.guard]
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@[grind]
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theorem guard_def (p : α → Bool) :
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Option.guard p = fun x => if p x then some x else none := rfl
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@ -614,10 +627,15 @@ end choice
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theorem or_eq_right_of_none {o o' : Option α} (h : o = none) : o.or o' = o' := by
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cases h; simp
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@[deprecated some_or (since := "2024-11-03")] theorem or_some : (some a).or o = some a := rfl
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/-- This will be renamed to `or_some` once the existing deprecated lemma is removed. -/
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@[simp, grind] theorem or_some' {o : Option α} : o.or (some a) = some (o.getD a) := by
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@[simp, grind] theorem or_some {o : Option α} : o.or (some a) = some (o.getD a) := by
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cases o <;> rfl
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@[deprecated or_some (since := "2025-05-03")]
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abbrev or_some' := @or_some
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@[simp, grind]
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theorem or_none : or o none = o := by
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cases o <;> rfl
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theorem or_eq_bif : or o o' = bif o.isSome then o else o' := by
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@ -645,10 +663,6 @@ abbrev or_eq_some := @or_eq_some_iff
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cases o₁ <;> cases o₂ <;> rfl
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instance : Std.Associative (or (α := α)) := ⟨@or_assoc _⟩
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@[simp, grind]
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theorem or_none : or o none = o := by
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cases o <;> rfl
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theorem or_eq_left_of_none {o o' : Option α} (h : o' = none) : o.or o' = o := by
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cases h; simp
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@ -838,7 +852,7 @@ end ite
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(o.map f).pbind g = o.pbind (fun x h => g (f x) (h ▸ rfl)) := by
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cases o <;> rfl
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@[simp] theorem pbind_eq_bind {α β : Type _} (o : Option α)
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@[simp, grind] theorem pbind_eq_bind {α β : Type _} (o : Option α)
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(f : α → Option β) : o.pbind (fun x _ => f x) = o.bind f := by
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cases o <;> rfl
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@ -898,7 +912,7 @@ theorem pbind_eq_some_iff {o : Option α} {f : (a : α) → o = some a → Optio
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· rintro ⟨h, rfl⟩
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rfl
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@[simp]
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@[simp, grind]
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theorem pmap_eq_map (p : α → Prop) (f : α → β) (o : Option α) (H) :
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@pmap _ _ p (fun a _ => f a) o H = Option.map f o := by
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cases o <;> simp
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@ -946,7 +960,7 @@ theorem pmap_congr {α : Type u} {β : Type v}
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@[simp, grind] theorem pelim_none : pelim none b f = b := rfl
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@[simp, grind] theorem pelim_some : pelim (some a) b f = f a rfl := rfl
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@[simp] theorem pelim_eq_elim : pelim o b (fun a _ => f a) = o.elim b f := by
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@[simp, grind] theorem pelim_eq_elim : pelim o b (fun a _ => f a) = o.elim b f := by
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cases o <;> simp
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@[simp, grind] theorem elim_pmap {p : α → Prop} (f : (a : α) → p a → β) (o : Option α)
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@ -1004,7 +1018,7 @@ theorem pfilter_eq_some_iff {α : Type _} {o : Option α} {p : (a : α) → o =
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· rintro ⟨⟨h, rfl⟩, h'⟩
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exact ⟨⟨o.get h, ⟨h, rfl⟩, h'⟩, rfl⟩
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@[simp] theorem pfilter_eq_filter {α : Type _} {o : Option α} {p : α → Bool} :
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@[simp, grind] theorem pfilter_eq_filter {α : Type _} {o : Option α} {p : α → Bool} :
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o.pfilter (fun a _ => p a) = o.filter p := by
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cases o with
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| none => rfl
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@ -1020,13 +1034,13 @@ theorem pfilter_eq_pbind_ite {α : Type _} {o : Option α}
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/-! ### LT and LE -/
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@[simp] theorem not_lt_none [LT α] {a : Option α} : ¬ a < none := by cases a <;> simp [LT.lt, Option.lt]
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@[simp] theorem none_lt_some [LT α] {a : α} : none < some a := by simp [LT.lt, Option.lt]
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@[simp] theorem some_lt_some [LT α] {a b : α} : some a < some b ↔ a < b := by simp [LT.lt, Option.lt]
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@[simp, grind] theorem not_lt_none [LT α] {a : Option α} : ¬ a < none := by cases a <;> simp [LT.lt, Option.lt]
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@[simp, grind] theorem none_lt_some [LT α] {a : α} : none < some a := by simp [LT.lt, Option.lt]
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@[simp, grind] theorem some_lt_some [LT α] {a b : α} : some a < some b ↔ a < b := by simp [LT.lt, Option.lt]
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@[simp] theorem none_le [LE α] {a : Option α} : none ≤ a := by cases a <;> simp [LE.le, Option.le]
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@[simp] theorem not_some_le_none [LE α] {a : α} : ¬ some a ≤ none := by simp [LE.le, Option.le]
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@[simp] theorem some_le_some [LE α] {a b : α} : some a ≤ some b ↔ a ≤ b := by simp [LE.le, Option.le]
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@[simp, grind] theorem none_le [LE α] {a : Option α} : none ≤ a := by cases a <;> simp [LE.le, Option.le]
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@[simp, grind] theorem not_some_le_none [LE α] {a : α} : ¬ some a ≤ none := by simp [LE.le, Option.le]
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@[simp, grind] theorem some_le_some [LE α] {a b : α} : some a ≤ some b ↔ a ≤ b := by simp [LE.le, Option.le]
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/-! ### min and max -/
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@ -3255,11 +3255,11 @@ theorem getEntry?_insertListIfNewUnit [BEq α] [PartialEquivBEq α] {l : List ((
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· simp
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· cases hc : containsKey hd l
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· simp only [Bool.not_false, Bool.and_self, ↓reduceIte, Option.some_or, cond_true,
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Option.or_some', Option.some.injEq]
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Option.or_some, Option.some.injEq]
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rw [getEntry?_eq_none.2, Option.getD_none]
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rwa [← containsKey_congr hhd]
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· simp only [Bool.not_true, Bool.and_false, Bool.false_eq_true, ↓reduceIte, cond_true,
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Option.or_some', getEntry?_eq_none]
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Option.or_some, getEntry?_eq_none]
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rw [containsKey_congr hhd, containsKey_eq_isSome_getEntry?] at hc
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obtain ⟨v, hv⟩ := Option.isSome_iff_exists.1 hc
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simp [hv]
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@ -7,7 +7,7 @@ set_option grind.warning false
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variable [BEq α] {o₁ o₂ o₃ o₄ o₅ : Option α}
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/--
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info: Try this: grind only [Option.some_or, Option.or_some', Option.or_assoc, Option.some_beq_none]
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info: Try this: grind only [Option.or_some, Option.some_or, Option.or_assoc, Option.some_beq_none]
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-/
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#guard_msgs in
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example : ((o₁.or (o₂.or (some x))).or (o₄.or o₅) == none) = false := by grind?
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@ -16,6 +16,10 @@ example : ((o₁.or (o₂.or (some x))).or (o₄.or o₅) == none) = false := by
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#guard_msgs in
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example : max (some 7) none = min (some 13) (some 7) := by grind?
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/-- info: Try this: grind only [Option.guard_pos] -/
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/-- info: Try this: grind only [Option.guard_def] -/
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#guard_msgs in
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example : Option.guard (· ≤ 7) 3 = some 3 := by grind? [Option.guard_pos]
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example : Option.guard (· ≤ 7) 3 = some 3 := by grind?
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/-- info: Try this: grind only [Option.mem_bind_iff] -/
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#guard_msgs in
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example {x : β} {o : Option α} {f : α → Option β} (h : a ∈ o) (h' : x ∈ f a) : x ∈ o.bind f := by grind?
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