aeddcbdc6d
See issue reported at https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/intro.20with.20type.20specified/near/305150215
39 lines
879 B
Text
39 lines
879 B
Text
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 (a : α) (s : Set α) :=
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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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theorem ext {a b : Set α} (h : ∀ (x : α), x ∈ a ↔ x ∈ b) : a = b :=
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funext (fun x => propext (h x))
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protected def subset (s₁ s₂ : Set α) :=
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∀ {a}, a ∈ s₁ → a ∈ s₂
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class Subset (α : Type u) where
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/-- Subset relation: `a ⊆ b` -/
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subset : α → α → Prop
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/-- Subset relation: `a ⊆ b` -/
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infix:50 " ⊆ " => Subset.subset
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instance : Subset (Set α) :=
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⟨Set.subset⟩
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instance : EmptyCollection (Set α) :=
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⟨λ _ => False⟩
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example (U : Type) (A B : Set U) : A ⊆ B → A = A :=
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fun h =>
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match @h with | (h : A ⊆ B) => sorry
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example (U : Type) (A B : Set U) : A ⊆ B → A = A := by
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intro (h : A ⊆ B)
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sorry
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