90bfd84a07
In the standard library, we should use explicit universe variables for universe polymorphic definitions. Users that want to declare universe polymorphic definitions but do not want to provide universe level parameters should use Type _ or Type*
25 lines
572 B
Text
25 lines
572 B
Text
prelude
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definition Prop : Type.{1} := Type.{0}
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section
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parameter A : Type*
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definition eq (a b : A) : Prop
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:= ∀P : A → Prop, P a → P b
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theorem subst (P : A → Prop) (a b : A) (H1 : eq a b) (H2 : P a) : P b
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:= H1 P H2
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theorem refl (a : A) : eq a a
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:= λ (P : A → Prop) (H : P a), H
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theorem symm (a b : A) (H : eq a b) : eq b a
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:= subst (λ x : A, eq x a) a b H (refl a)
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theorem trans (a b c : A) (H1 : eq a b) (H2 : eq b c) : eq a c
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:= subst (λ x : A, eq a x) b c H2 H1
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end
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check subst.{1}
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check refl.{1}
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check symm.{1}
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check trans.{1}
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