18 lines
573 B
Text
18 lines
573 B
Text
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import .LES_of_homotopy_groups homotopy.connectedness homotopy.homotopy_group
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open eq is_trunc pointed homotopy is_equiv fiber equiv trunc nat
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namespace is_conn
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theorem is_contr_HG_fiber_of_is_connected {A B : Type*} (n k : ℕ) (f : A →* B)
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[H : is_conn_map n f] (H2 : k ≤ n) : is_contr (π[k] (pfiber f)) :=
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@(trivial_homotopy_group_of_is_conn (pfiber f) H2) (H pt)
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theorem is_equiv_π_of_is_connected {A B : Type*} (n k : ℕ) (f : A →* B)
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[H : is_conn_map n f] (H : k ≤ n) : is_equiv (π→[k] f) :=
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begin
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exact sorry
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end
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end is_conn
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