3f98f6bc07
This PR changes how `{...}`/`where` notation ("structure instance
notation") elaborates. The notation now tries to simulate a flat
representation as much as possible, without exposing the details of
subobjects. Features:
- When fields are elaborated, their expected types now have a couple
reductions applied. For all projections and constructors associated to
the structure and its parents, projections of constructors are reduced
and constructors of projections are eta reduced, and also implementation
detail local variables are zeta reduced in propositions (so tactic
proofs should never see them anymore). Furthermore, field values are
beta reduced automatically in successive field types. The example in
[mathlib4#12129](https://github.com/leanprover-community/mathlib4/issues/12129#issuecomment-2056134533)
now shows a goal of `0 = 0` rather than `{ toFun := fun x => x }.toFun 0
= 0`.
- All parents can now be used as field names, not just the subobject
parents. These are like additional sources but with three constraints:
every field of the value must be used, the fields must not overlap with
other provided fields, and every field of the specified parent must be
provided for. Similar to sources, the values are hoisted to `let`s if
they are not already variables, to avoid multiple evaluation. They are
implementation detail local variables, so they get unfolded for
successive fields.
- All class parents are now used to fill in missing fields, not just the
subobject parents. Closes #6046. Rules: (1) only those parents whose
fields are a subset of the remaining fields are considered, (2) parents
are considered only before any fields are elaborated, and (3) only those
parents whose type can be computed are considered (this can happen if a
parent depends on another parent, which is possible since #7302).
- Default values and autoparams now respect the resolution order
completely: each field has at most one default value definition that can
provide for it. The algorithm that tries to unstick default values by
walking up the subobject hierarchy has been removed. If there are
applications of default value priorities, we might consider it in a
future release.
- The resulting constructors are now fully packed. This is implemented
by doing structure eta reduction of the elaborated expressions.
- "Magic field definitions" (as reported [on
Zulip](https://leanprover.zulipchat.com/#narrow/channel/113489-new-members/topic/Where.20is.20sSup.20defined.20on.20submodules.3F/near/499578795))
have been eliminated. This was where fields were being solved for by
unification, tricking the default value system into thinking they had
actually been provided. Now the default value system keeps track of
which fields it has actually solved for, and which fields the user did
not provide. Explicit structure fields (the default kind) without any
explicit value definition will result in an error. If it was solved for
by unification, the error message will include the inferred value, like
"field 'f' must be explicitly provided, its synthesized value is v"
- When the notation is used in patterns, it now no longer inserts fields
using class parents, and it no longer applies autoparams or default
values. The motivation is that one expects patterns to match only the
given fields. This is still imperfect, since fields might be solved for
indirectly.
- Elaboration now attempts error recovery. Extraneous fields log errors
and are ignored, missing fields are filled with `sorry`.
This is a breaking change, but generally the mitigation is to remove
`dsimp only` from the beginnings of proofs. Sometimes "magic fields"
need to be provided — four possible mitigations are (1) to provide the
field, (2) to provide `_` for the value of the field, (3) to add `..` to
the structure instance notation, (4) or decide to modify the `structure`
command to make the field implicit. Lastly, sometimes parent instances
don't apply when they should. This could be because some of the provided
fields overlap with the class, or it could be that the parent depends on
some of the fields for synthesis — and as parents are only considered
before any fields are elaborated, such parents might not be possible to
use — we will look into refining this further.
There is also a change to elaboration: now the `afterTypeChecking`
attributes are run with all `structure` data set up (e.g. the list of
parents, along with all parent projections in the environment). This is
necessary since attributes like `@[ext]` use structure instance
notation, and the notation needs all this data to be set up now.
206 lines
7.3 KiB
Text
206 lines
7.3 KiB
Text
instance {ι : Type u} {α : ι → Type v} [∀ i, LE (α i)] : LE (∀ i, α i) where
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le x y := ∀ i, x i ≤ y i
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class Top (α : Type u) where
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top : α
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class Bot (α : Type u) where
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bot : α
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notation "⊤" => Top.top
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notation "⊥" => Bot.bot
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class Preorder (α : Type u) extends LE α, LT α where
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le_refl : ∀ a : α, a ≤ a
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le_trans : ∀ a b c : α, a ≤ b → b ≤ c → a ≤ c
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lt := λ a b => a ≤ b ∧ ¬ b ≤ a
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lt_iff_le_not_le : ∀ a b : α, a < b ↔ (a ≤ b ∧ ¬ b ≤ a)
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class PartialOrder (α : Type u) extends Preorder α :=
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(le_antisymm : ∀ a b : α, a ≤ b → b ≤ a → a = b)
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def Set (α : Type u) := α → Prop
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def setOf {α : Type u} (p : α → Prop) : Set α :=
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p
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namespace Set
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protected def Mem (s : Set α) (a : α) : Prop :=
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s a
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instance : Membership α (Set α) :=
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⟨Set.Mem⟩
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def range (f : ι → α) : Set α :=
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setOf (λ x => ∃ y, f y = x)
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end Set
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class InfSet (α : Type _) where
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infₛ : Set α → α
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class SupSet (α : Type _) where
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supₛ : Set α → α
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export SupSet (supₛ)
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export InfSet (infₛ)
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open Set
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def supᵢ {α : Type _} [SupSet α] {ι} (s : ι → α) : α :=
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supₛ (range s)
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def infᵢ {α : Type _} [InfSet α] {ι} (s : ι → α) : α :=
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infₛ (range s)
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class HasSup (α : Type u) where
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sup : α → α → α
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class HasInf (α : Type u) where
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inf : α → α → α
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@[inherit_doc]
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infixl:68 " ⊔ " => HasSup.sup
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@[inherit_doc]
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infixl:69 " ⊓ " => HasInf.inf
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class SemilatticeSup (α : Type u) extends HasSup α, PartialOrder α where
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protected le_sup_left : ∀ a b : α, a ≤ a ⊔ b
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protected le_sup_right : ∀ a b : α, b ≤ a ⊔ b
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protected sup_le : ∀ a b c : α, a ≤ c → b ≤ c → a ⊔ b ≤ c
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class SemilatticeInf (α : Type u) extends HasInf α, PartialOrder α where
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protected inf_le_left : ∀ a b : α, a ⊓ b ≤ a
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protected inf_le_right : ∀ a b : α, a ⊓ b ≤ b
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protected le_inf : ∀ a b c : α, a ≤ b → a ≤ c → a ≤ b ⊓ c
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class Lattice (α : Type u) extends SemilatticeSup α, SemilatticeInf α
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class CompleteSemilatticeInf (α : Type _) extends PartialOrder α, InfSet α where
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infₛ_le : ∀ s, ∀ a, a ∈ s → infₛ s ≤ a
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le_infₛ : ∀ s a, (∀ b, b ∈ s → a ≤ b) → a ≤ infₛ s
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class CompleteSemilatticeSup (α : Type _) extends PartialOrder α, SupSet α where
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le_supₛ : ∀ s, ∀ a, a ∈ s → a ≤ supₛ s
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supₛ_le : ∀ s a, (∀ b, b ∈ s → b ≤ a) → supₛ s ≤ a
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class CompleteLattice (α : Type _) extends Lattice α, CompleteSemilatticeSup α,
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CompleteSemilatticeInf α, Top α, Bot α where
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protected le_top : ∀ x : α, x ≤ ⊤
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protected bot_le : ∀ x : α, ⊥ ≤ x
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class Frame (α : Type _) extends CompleteLattice α where
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class Coframe (α : Type _) extends CompleteLattice α where
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infᵢ_sup_le_sup_infₛ (a : α) (s : Set α) : (infᵢ (λ b => a ⊔ b)) ≤ a ⊔ infₛ s
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-- should be ⨅ b ∈ s but I had problems with notation
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class CompleteDistribLattice (α : Type _) extends Frame α where
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infᵢ_sup_le_sup_infₛ : ∀ a s, (infᵢ (λ b => a ⊔ b)) ≤ a ⊔ infₛ s
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-- similarly this is not quite right mathematically but this doesn't matter
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-- See note [lower instance priority]
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instance (priority := 100) CompleteDistribLattice.toCoframe {α : Type _} [CompleteDistribLattice α] :
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Coframe α :=
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{ ‹CompleteDistribLattice α› with }
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class OrderTop (α : Type u) [LE α] extends Top α where
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le_top : ∀ a : α, a ≤ ⊤
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class OrderBot (α : Type u) [LE α] extends Bot α where
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bot_le : ∀ a : α, ⊥ ≤ a
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class BoundedOrder (α : Type u) [LE α] extends OrderTop α, OrderBot α
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instance(priority := 100) CompleteLattice.toBoundedOrder {α : Type _} [h : CompleteLattice α] :
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BoundedOrder α :=
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{ h with }
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namespace Pi
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variable {ι : Type _} {α' : ι → Type _}
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instance [∀ i, Bot (α' i)] : Bot (∀ i, α' i) :=
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⟨fun _ => ⊥⟩
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instance [∀ i, Top (α' i)] : Top (∀ i, α' i) :=
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⟨fun _ => ⊤⟩
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protected instance LE {ι : Type u} {α : ι → Type v} [∀ i, LE (α i)] : LE (∀ i, α i) where
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le x y := ∀ i, x i ≤ y i
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instance Preorder {ι : Type u} {α : ι → Type v} [∀ i, Preorder (α i)] : Preorder (∀ i, α i) :=
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{ Pi.LE with
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le_refl := sorry
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le_trans := sorry
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lt_iff_le_not_le := sorry }
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instance PartialOrder {ι : Type u} {α : ι → Type v} [∀ i, PartialOrder (α i)] :
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PartialOrder (∀ i, α i) :=
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{ Pi.Preorder with
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le_antisymm := sorry }
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instance semilatticeSup [∀ i, SemilatticeSup (α' i)] : SemilatticeSup (∀ i, α' i) where
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sup x y i := x i ⊔ y i
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le_sup_left _ _ _ := SemilatticeSup.le_sup_left _ _
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le_sup_right _ _ _ := SemilatticeSup.le_sup_right _ _
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sup_le _ _ _ ac bc i := SemilatticeSup.sup_le _ _ _ (ac i) (bc i)
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instance semilatticeInf [∀ i, SemilatticeInf (α' i)] : SemilatticeInf (∀ i, α' i) where
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inf x y i := x i ⊓ y i
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inf_le_left _ _ _ := SemilatticeInf.inf_le_left _ _
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inf_le_right _ _ _ := SemilatticeInf.inf_le_right _ _
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le_inf _ _ _ ac bc i := SemilatticeInf.le_inf _ _ _ (ac i) (bc i)
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instance lattice [∀ i, Lattice (α' i)] : Lattice (∀ i, α' i) :=
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{ Pi.semilatticeSup, Pi.semilatticeInf with }
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instance orderTop [∀ i, LE (α' i)] [∀ i, OrderTop (α' i)] : OrderTop (∀ i, α' i) :=
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{ inferInstanceAs (Top (∀ i, α' i)) with le_top := sorry }
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instance orderBot [∀ i, LE (α' i)] [∀ i, OrderBot (α' i)] : OrderBot (∀ i, α' i) :=
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{ inferInstanceAs (Bot (∀ i, α' i)) with bot_le := sorry }
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instance boundedOrder [∀ i, LE (α' i)] [∀ i, BoundedOrder (α' i)] : BoundedOrder (∀ i, α' i) :=
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{ Pi.orderTop, Pi.orderBot with }
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instance SupSet {α : Type _} {β : α → Type _} [∀ i, SupSet (β i)] : SupSet (∀ i, β i) :=
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⟨fun s i => supᵢ (λ (f : {f : ∀ i, β i // f ∈ s}) => f.1 i)⟩
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instance InfSet {α : Type _} {β : α → Type _} [∀ i, InfSet (β i)] : InfSet (∀ i, β i) :=
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⟨fun s i => infᵢ (λ (f : {f : ∀ i, β i // f ∈ s}) => f.1 i)⟩
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instance completeLattice {α : Type _} {β : α → Type _} [∀ i, CompleteLattice (β i)] :
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CompleteLattice (∀ i, β i) :=
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{ Pi.boundedOrder, Pi.lattice with
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le_supₛ := sorry
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infₛ_le := sorry
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supₛ_le := sorry
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le_infₛ := sorry
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}
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instance frame {ι : Type _} {π : ι → Type _} [∀ i, Frame (π i)] : Frame (∀ i, π i) :=
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{ Pi.completeLattice with }
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instance coframe {ι : Type _} {π : ι → Type _} [∀ i, Coframe (π i)] : Coframe (∀ i, π i) :=
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{ Pi.completeLattice with infᵢ_sup_le_sup_infₛ := sorry }
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end Pi
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-- very quick (instantaneous) in Lean 4
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instance Pi.completeDistribLattice' {ι : Type _} {π : ι → Type _}
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[∀ i, CompleteDistribLattice (π i)] : CompleteDistribLattice (∀ i, π i) :=
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CompleteDistribLattice.mk (Pi.coframe.infᵢ_sup_le_sup_infₛ)
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-- User: takes around 2 seconds wall clock time on my PC (but very quick in Lean 3)
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set_option maxHeartbeats 400 -- make sure it stays fast
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set_option synthInstance.maxHeartbeats 400
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instance Pi.completeDistribLattice'' {ι : Type _} {π : ι → Type _}
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[∀ i, CompleteDistribLattice (π i)] : CompleteDistribLattice (∀ i, π i) :=
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{ Pi.frame, Pi.coframe with }
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-- quick Lean 3 version:
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-- https://github.com/leanprover-community/mathlib/blob/b26e15a46f1a713ce7410e016d50575bb0bc3aa4/src/order/complete_boolean_algebra.lean#L210
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