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feat(library/init/data/prod): has_lt for prod

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This commit is contained in:
Leonardo de Moura 2017-11-13 15:51:14 -08:00
parent a39c0531cf
commit 2c8a901df9
1 changed files with 19 additions and 6 deletions
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25
library/init/data/prod.lean
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@ -7,10 +7,12 @@ prelude
import init.logic
universes u v
instance {α : Type u} {β : Type v} [inhabited α] [inhabited β] : inhabited (prod α β) :=
section
variables {α : Type u} {β : Type v}
instance [inhabited α] [inhabited β] : inhabited (prod α β) :=
⟨(default α, default β)⟩
instance {α : Type u} {β : Type v} [h₁ : decidable_eq α] [h₂ : decidable_eq β] : decidable_eq (α × β)
instance [h₁ : decidable_eq α] [h₂ : decidable_eq β] : decidable_eq (α × β)
| (a, b) (a', b') :=
match (h₁ a a') with
| (is_true e₁) :=
@ -21,10 +23,21 @@ instance {α : Type u} {β : Type v} [h₁ : decidable_eq α] [h₂ : decidable_
| (is_false n₁) := is_false (assume h, prod.no_confusion h (λ e₁' e₂', absurd e₁' n₁))
end
namespace prod
instance [has_lt α] [has_lt β] : has_lt (α × β) :=
⟨λ s t, s.1 < t.1 ∨ (s.1 = t.1 ∧ s.2 < t.2)⟩
def {u₁ u₂ v₁ v₂} map {α₁ : Type u₁} {α₂ : Type u₂} {β₁ : Type v₁} {β₂ : Type v₂}
instance prod_has_decidable_lt
[has_lt α] [has_lt β]
[decidable_eq α] [decidable_eq β]
[decidable_rel ((<) : α → α → Prop)]
[decidable_rel ((<) : β → β → Prop)] : Π s t : α × β, decidable (s < t) :=
λ t s, or.decidable
lemma prod.lt_def [has_lt α] [has_lt β] (s t : α × β) : (s < t) = (s.1 < t.1 ∨ (s.1 = t.1 ∧ s.2 < t.2)) :=
rfl
end
def {u₁ u₂ v₁ v₂} prod.map {α₁ : Type u₁} {α₂ : Type u₂} {β₁ : Type v₁} {β₂ : Type v₂}
(f : α₁ → α₂) (g : β₁ → β₂) : α₁ × β₁ → α₂ × β₂
| (a, b) := (f a, g b)
end prod