2015-03-12 07:31:10 +00:00
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open eq is_equiv funext
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constant f : nat → nat → nat
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example : (λ x y : nat, f x y) = f :=
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rfl
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namespace hide
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variables {A : Type} {B : A → Type} {C : Πa, B a → Type}
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definition homotopy2 [reducible] (f g : Πa b, C a b) : Type :=
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Πa b, f a b = g a b
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notation f `∼2`:50 g := homotopy2 f g
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definition eq_of_homotopy2 {f g : Πa b, C a b} (H : f ∼2 g) : f = g :=
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eq_of_homotopy (λa, eq_of_homotopy (H a))
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definition apD100 {f g : Πa b, C a b} (p : f = g) : f ∼2 g :=
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λa b, apD10 (apD10 p a) b
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local attribute eq_of_homotopy [reducible]
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definition foo (f g : Πa b, C a b) (H : f ∼2 g) (a : A)
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: apD100 (eq_of_homotopy2 H) a = H a :=
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begin
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2015-03-28 00:26:06 +00:00
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esimp [apD100, eq_of_homotopy2, eq_of_homotopy],
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2015-03-12 07:31:10 +00:00
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rewrite (retr apD10 (λ(a : A), eq_of_homotopy (H a))),
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apply (retr apD10)
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end
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end hide
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