feat(library/hott): use new 'parameters' command
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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1 changed files with 5 additions and 13 deletions
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@ -78,14 +78,9 @@ theorem ap_refl {A : Type} {B : Type} (f : A → B) (a : A) : ap f (refl a) = re
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:= refl (refl (f a))
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section
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parameter {A : Type}
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parameter {B : Type}
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parameter {C : Type}
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parameter f : A → B
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parameter g : B → C
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parameters x y z : A
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parameter p : x = y
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parameter q : y = z
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parameters {A : Type} {B : Type} {C : Type}
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parameters (f : A → B) (g : B → C)
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parameters (x y z : A) (p : x = y) (q : y = z)
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theorem ap_trans_dist : ap f (p ⬝ q) = (ap f p) ⬝ (ap f q)
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:= have e1 : ap f (p ⬝ refl y) = (ap f p) ⬝ (ap f (refl y)), from refl _,
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@ -105,9 +100,7 @@ section
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end
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section
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parameter {A : Type}
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parameter {B : A → Type}
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parameter f : Π x, B x
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parameters {A : Type} {B : A → Type} (f : Π x, B x)
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definition D [private] (x y : A) (p : x = y) := p*(f x) = f y
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definition d [private] (x : A) : D x x (refl x)
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:= refl (f x)
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@ -129,8 +122,7 @@ notation `assume` binders `,` r:(scoped f, f) := r
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notation `take` binders `,` r:(scoped f, f) := r
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section
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parameter {A : Type}
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parameter {B : Type}
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parameters {A : Type} {B : Type}
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theorem hom_refl (f : A → B) : f ∼ f
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:= take x, refl (f x)
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