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use pointed_reduce in functor_smash_homotopic
Signed-off-by: Ali Caglayan <[email protected]> <!-- ps-id: 36a879a1-5c54-41f2-9335-1e326f5f8fc0 -->
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theories/Homotopy/Smash.v

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@@ -294,6 +294,9 @@ Definition functor_smash_homotopic {X Y A B : pType}
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(p : f $== h) (q : g $== k)
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: functor_smash f g $== functor_smash h k.
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Proof.
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destruct f as [f f_eq], g as [g g_eq].
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revert p q.
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pointed_reduce.
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snrapply Build_pHomotopy.
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{ snrapply Smash_ind.
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- intros x y.
@@ -346,8 +349,8 @@ Proof.
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2: apply concat_Vp.
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symmetry.
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nrapply ap_sm_right. }
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simpl.
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by pelim p q f g h k.
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lhs nrapply (ap022 _ (dpoint_eq p) (dpoint_eq q)).
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rapply ap011_pp.
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Defined.
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Global Instance is0bifunctor_smash : IsBifunctor Smash.

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